Qwen2-Math 72B on 4.MD.A.3
Common Core Standard 4.MD.A.3
This standard covers the following:
Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
Problem: A rectangle has a length of 21m and a width of 37m. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 x (length + width) = 2 x (21m + 37m) = 2 x 58m = <<2*58=116>>116m ### Answer: 116m
Expected answer: 116
Correct? Yes
Problem: Now consider that the length of the rectangle has changed to 4m while the width remains at 37m. What is the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 x (length + width) = 2 x (4m + 37m) = 2 x 41m = <<2*41=82>>82m ### Answer: 82m
Expected answer: 82
Correct? Yes
Problem: A rectangular garden has a length of 50 feet and a width of 20 feet. What is the perimeter of the garden?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding up all its sides. Since a rectangle has two lengths and two widths, the formula for the perimeter is P = 2L + 2W, where L is the length and W is the width. In this case, the length is 50 feet and the width is 20 feet. So, the perimeter is P = 2(50) + 2(20) = 100 + 40 = <<100+40=140>>140 feet. ### Answer: 140
Expected answer: 140
Correct? Yes
Problem: A landscaper plans to reduce the length of the rectangular garden to 15 feet while keeping the width the same. What will the new perimeter of the garden be?
Qwen2-Math 72B:
Reasoning: The new length of the garden is 15 feet, and the width remains 20 feet. Using the same formula for the perimeter, P = 2L + 2W, we can calculate the new perimeter as P = 2(15) + 2(20) = 30 + 40 = <<30+40=70>>70 feet. ### Answer: 70
Expected answer: 70
Correct? Yes
Problem: A rectangle has a width of 7m and a length of 26m. What is the area of this rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 26m x 7m Area = 182 square meters ### Answer: 182 square meters
Expected answer: 182
Correct? Yes
Problem: The width of the rectangle stays the same at 7m, but the length extends by 9m to become 35m. What is the area of the rectangle now?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 35m x 7m Area = 245 square meters ### Answer: 245 square meters
Expected answer: 245
Correct? Yes
Problem: A rectangle has a length of 50m and a width of 15m. What is its perimeter?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 x (length + width) = 2 x (50m + 15m) = 2 x 65m = 130m ### Answer: 130m
Expected answer: 130
Correct? Yes
Problem: The rectangle mentioned in the previous problem had its width reduced to 9m while the length remained the same. What is the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 x (length + width) = 2 x (50m + 9m) = 2 x 59m = 118m ### Answer: 118m
Expected answer: 118
Correct? Yes
Problem: A rectangular fence has a side length of 5m and another side of 19m. What is the total distance, in meters, around the fence (perimeter)?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. Since a rectangle has two pairs of equal sides, the total distance around the fence is 2*(5m + 19m) = <<2*(5+19)=68>>68 meters. ### Answer: 68 meters
Expected answer: 48
Correct? No
Problem: A rectangle has sides of length 49m and 6m. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. Therefore, the perimeter is 2*(49m + 6m) = <<2*(49+6)=110>>110m. ### Answer: 110m
Expected answer: 110
Correct? Yes
Problem: Suppose we were mistaken in the original measurement, and one side of the rectangle was actually 17m instead of 49m. What would the new perimeter of the rectangle be?
Qwen2-Math 72B:
Reasoning: The new perimeter of the rectangle would be 2*(17m + 6m) = <<2*(17+6)=46>>46m. ### Answer: 46m
Expected answer: 46
Correct? Yes
Problem: Joshua plans to lay a wire around his rectangular garden. If the garden is 7m wide and 26m long, how much wire will Joshua need to enclose the garden completely?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two pairs of equal sides, the formula for the perimeter is P = 2*(length + width). In this case, the length of the garden is 26m and the width is 7m. So, the perimeter of the garden is P = 2*(26m + 7m) = 2*33m = 66m. Therefore, Joshua will need 66 meters of wire to enclose the garden completely. ### Answer: 66
Expected answer: 66
Correct? Yes
Problem: A rectangle has a length of 18 meters and a width of 11 meters. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. The formula for the perimeter of a rectangle is P = 2(l + w), where l is the length and w is the width. Given that the length (l) is 18 meters and the width (w) is 11 meters, we can substitute these values into the formula: P = 2(18 + 11) = 2(29) = 58 meters. ### Answer: 58 meters
Expected answer: 58
Correct? Yes
Problem: Suppose the width of the rectangle changed to 44 meters, while the length remained at 18 meters. What would be the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: Using the same formula for the perimeter of a rectangle, P = 2(l + w), we can substitute the new width (w) of 44 meters and the unchanged length (l) of 18 meters: P = 2(18 + 44) = 2(62) = 124 meters. ### Answer: 124 meters
Expected answer: 124
Correct? Yes
Problem: The dimensions of a rectangle are 22 feet by 39 feet. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter can be calculated as 2*(length + width). The perimeter of the rectangle is 2*(22+39) = <<2*(22+39)=122>>122 feet. ### Answer: 122
Expected answer: 122
Correct? Yes
Problem: If the length of the rectangle is now 26 feet instead of 39 feet, while the width remains the same at 22 feet, what would then be the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter can be calculated as 2*(length + width). The new perimeter of the rectangle is 2*(26+22) = <<2*(26+22)=96>>96 feet. ### Answer: 96
Expected answer: 96
Correct? Yes
Problem: A rectangle has two sides measuring 45m and the other two sides measuring 25m each. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. Therefore, the perimeter is 45m + 45m + 25m + 25m = <<45+45+25+25=140>>140m. ### Answer: 140m
Expected answer: 140
Correct? Yes
Problem: In the previous rectangle question, suppose one of the sides measuring 45m was incorrectly assessed. The actual measurement is found to be 42m. With this new information, what would be the adjusted perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: With the corrected side length, the perimeter is now calculated as 42m + 42m + 25m + 25m = <<42+42+25+25=134>>134m. ### Answer: 134m
Expected answer: 134
Correct? Yes
Problem: A rectangular garden has a length of 8m and a width of 5m. What is the perimeter of this garden?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. For this garden, the perimeter is 2*(8m + 5m) = <<2*(8+5)=26>>26m. ### Answer: 26m
Expected answer: 26
Correct? Yes
Problem: The owner of the rectangular garden decided to extend its length to 46m while keeping the width the same, i.e., 5m. What is the new perimeter of the garden now?
Qwen2-Math 72B:
Reasoning: The new perimeter of the garden is calculated by adding all its sides. For the extended garden, the perimeter is 2*(46m + 5m) = <<2*(46+5)=102>>102m. ### Answer: 102m
Expected answer: 102
Correct? Yes
Problem: In a rectangle, the length is 19 units and the width is 17 units. What is the area of this rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length × width = 19 × 17 = <<19*17=323>>323 square units. ### Answer: 323
Expected answer: 323
Correct? Yes
Problem: In the previous rectangle problem, what if the length was 22 units instead of 19 units while the width remained the same at 17 units? What would be the new area of the rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length × width = 22 × 17 = <<22*17=374>>374 square units. ### Answer: 374
Expected answer: 374
Correct? Yes
Problem: A rectangle has a length of 42 meters and a width of 8 meters. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 x (length + width) Perimeter = 2 x (42 + 8) Perimeter = 2 x 50 Perimeter = 100 meters ### Answer: 100
Expected answer: 100
Correct? Yes
Problem: A rectangle has a width of 16m and a length of 38m. What is the area of this rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 38m x 16m Area = 608m² ### Answer: 608m²
Expected answer: 608
Correct? Yes
Problem: In the rectangle from the previous problem, suppose we replace the length of 38m with a new length of 22m. What would the new area of the rectangle be?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 22m x 16m Area = 352m² ### Answer: 352m²
Expected answer: 352
Correct? Yes
Problem: Consider a rectangular plot of land. The plot has a length of 28m and a width of 17m. What is the area of the plot?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the plot is 28m * 17m = <<28*17=476>>476 square meters. ### Answer: 476 square meters
Expected answer: 476
Correct? Yes
Problem: Suppose instead of the original 28m, the length of the rectangular plot of land were only 10m while keeping the width the same at 17m. What would then be the area of the rectangular plot of land?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the plot is 10m * 17m = <<10*17=170>>170 square meters. ### Answer: 170 square meters
Expected answer: 170
Correct? Yes
Problem: A rectangle has a length of 43m and a width of 41m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. So, the perimeter is 43+41+43+41 = <<43+41+43+41=168>>168m. ### Answer: 168
Expected answer: 168
Correct? Yes
Problem: Suppose the rectangle from the previous problem had its length reduced to 18m while keeping the width the same. What would be the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The new perimeter would be 18+41+18+41 = <<18+41+18+41=118>>118m. ### Answer: 118
Expected answer: 118
Correct? Yes
Problem: A rectangle has one side that measures 44m, and the other side that measures 17m. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding up all its sides. Since a rectangle has two pairs of equal sides, the perimeter is 2*(44m + 17m) = <<2*(44+17)=122m>>122m. ### Answer: 122m
Expected answer: 122
Correct? Yes
Problem: In the previous problem, we considered a rectangle with one side that measures 44m, and the other side that measures 17m. What would be the perimeter of the rectangle if instead the length of the second side were 21m?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding up all its sides. Since a rectangle has two pairs of equal sides, the perimeter is 2*(44m + 21m) = <<2*(44+21)=130m>>130m. ### Answer: 130m
Expected answer: 130
Correct? Yes
Problem: A rectangle's perimeter is twice the sum of its width and length. If the rectangle's width is 2m and its length is 20m, what is its perimeter?
Qwen2-Math 72B:
Reasoning: The sum of the rectangle's width and length is 2+20 = <<2+20=22>>22m. The rectangle's perimeter is twice the sum of its width and length, so its perimeter is 2*22 = <<2*22=44>>44m. ### Answer: 44
Expected answer: 44
Correct? Yes
Problem: If the width of the rectangle is increased from 2m to 32m, while keeping the length the same at 20m, what is the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The new sum of the rectangle's width and length is 32+20 = <<32+20=52>>52m. The rectangle's perimeter is twice the sum of its width and length, so its new perimeter is 2*52 = <<2*52=104>>104m. ### Answer: 104
Expected answer: 104
Correct? Yes
Problem: A rectangle has a length of 4 meters and a width of 5 meters. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding up all its sides. Since a rectangle has two lengths and two widths, the formula for the perimeter is 2(length + width). Perimeter = 2(4 + 5) = 2(9) = <<2*9=18>>18 meters. ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: Consider the same rectangle from before, but now suppose its length is extended to 42 meters while the width remains 5 meters. What would then be the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding up all its sides. Since a rectangle has two lengths and two widths, the formula for the perimeter is 2(length + width). Perimeter = 2(42 + 5) = 2(47) = <<2*47=94>>94 meters. ### Answer: 94
Expected answer: 94
Correct? Yes
Problem: A rectangle has a length of 45m and a width of 37m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 * (length + width) = 2 * (45m + 37m) = 2 * 82m = 164m ### Answer: 164m
Expected answer: 164
Correct? Yes
Problem: If the length of the rectangle remains the same at 45m, but the width is increased to 47m, what would be the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 * (length + width) = 2 * (45m + 47m) = 2 * 92m = 184m ### Answer: 184m
Expected answer: 184
Correct? Yes
Problem: A rectangle has a length of 27m and a width of 21m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. For a rectangle with length L and width W, the perimeter P is given by P = 2L + 2W. Given L = 27m and W = 21m, the perimeter is P = 2(27) + 2(21) = 54 + 42 = <<54+42=96>>96m. ### Answer: 96m
Expected answer: 96
Correct? Yes
Problem: Suppose we extended the length of the rectangle from the previous problem to 45m, while keeping the width at 21m. What would the new perimeter of this rectangle be?
Qwen2-Math 72B:
Reasoning: With the new length L = 45m and the width W = 21m, the perimeter P is calculated as P = 2L + 2W = 2(45) + 2(21) = 90 + 42 = <<90+42=132>>132m. ### Answer: 132m
Expected answer: 132
Correct? Yes
Problem: A rectangular garden has a length of 30m and a width of 20m. What is the perimeter of the garden?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the formula for the perimeter is P = 2L + 2W, where L is the length and W is the width. In this case, the length of the garden is 30m and the width is 20m. Plugging these values into the formula, we get: P = 2(30m) + 2(20m) P = 60m + 40m P = 100m Therefore, the perimeter of the garden is 100m. ### Answer: 100m
Expected answer: 100
Correct? Yes
Problem: Suppose the width of the rectangular garden is increased to 48m, while the length remains the same at 30m. What would be the new perimeter of the garden?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the formula for the perimeter is P = 2L + 2W, where L is the length and W is the width. In this case, the length of the garden is 30m and the width is 48m. Plugging these values into the formula, we get: P = 2(30m) + 2(48m) P = 60m + 96m P = 156m Therefore, the new perimeter of the garden is 156m. ### Answer: 156m
Expected answer: 156
Correct? Yes
Problem: A rectangle has a length of 30m and a width of 27m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. For a rectangle, this means adding the length and the width, and then doubling the sum because there are two of each. Perimeter = 2 * (Length + Width) = 2 * (30m + 27m) = 2 * 57m = <<2*57=114>>114m. ### Answer: 114m
Expected answer: 114
Correct? Yes
Problem: A rectangle has a length of 23m and a width of 11m. What is the area of this rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 23m x 11m Area = 253 square meters ### Answer: 253 square meters
Expected answer: 253
Correct? Yes
Problem: A rectangle has a length of 3m and a width of 9m. What would be the total perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. In this case, the rectangle has two sides that are 3m long and two sides that are 9m long. So, the perimeter would be 2*(3m + 9m) = 2*12m = 24m. ### Answer: 24m
Expected answer: 24
Correct? Yes
Problem: Continuing from the previous problem, suppose the length of the rectangle is still 3m, but now the width has increased to 13m. What is the new total perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. In this case, the rectangle has two sides that are 3m long and two sides that are 13m long. So, the perimeter would be 2*(3m + 13m) = 2*16m = 32m. ### Answer: 32m
Expected answer: 32
Correct? Yes
Problem: A rectangle has a length of 31m and a width of 6m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. For this rectangle, the perimeter is 2*(length + width) = 2*(31m + 6m) = 2*37m = <<2*37=74>>74m. ### Answer: 74m
Expected answer: 74
Correct? Yes
Problem: Now consider, if instead of a length of 31m, the rectangle had a length of 43m but the width remained the same at 6m. What would be the new perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. For this rectangle, the perimeter is 2*(length + width) = 2*(43m + 6m) = 2*49m = <<2*49=98>>98m. ### Answer: 98m
Expected answer: 98
Correct? Yes
Problem: A rectangle has a length of 12m and a width of 33m. What is the area of this rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 12m x 33m Area = 396 square meters ### Answer: 396 square meters
Expected answer: 396
Correct? Yes
Problem: Now, consider that the length of the rectangle was initially 18m instead of 12m, while the width remains the same at 33m. What would be the area of the rectangle in this scenario?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 18m x 33m Area = 594 square meters ### Answer: 594 square meters
Expected answer: 594
Correct? Yes
Problem: A rectangle has a length of 20m and all of its sides are of equal length. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: Since all sides of a rectangle are of equal length, the width of the rectangle is also 20m. The perimeter of a rectangle is calculated as 2*(length + width). Therefore, the perimeter of this rectangle is 2*(20+20) = <<2*(20+20)=80>>80m. ### Answer: 80
Expected answer: 80
Correct? Yes
Problem: A rectangular playground has a length of 35m and a width of 9m. What is the perimeter of the playground?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the formula for the perimeter is P = 2l + 2w, where l is the length and w is the width. In this case, the length of the playground is 35m and the width is 9m. So, the perimeter is P = 2(35) + 2(9) = 70 + 18 = <<70+18=88>>88m. ### Answer: 88
Expected answer: 88
Correct? Yes
Problem: Suppose the length of the rectangular playground was initially stated incorrectly and it's actually 26m, while the width remains 9m. What would be the correct perimeter of the playground in this case?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the formula for the perimeter is P = 2l + 2w, where l is the length and w is the width. In this case, the length of the playground is 26m and the width is 9m. So, the perimeter is P = 2(26) + 2(9) = 52 + 18 = <<52+18=70>>70m. ### Answer: 70
Expected answer: 70
Correct? Yes
Problem: A rectangle has a length of 9m and a width of 25m. What is the area of the rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 9m x 25m Area = 225 square meters ### Answer: 225 square meters
Expected answer: 225
Correct? Yes
Problem: Suppose the length of the rectangle was actually 16m and the width remained the same at 9m. What would be the new area of the rectangle in this case?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 16m x 9m Area = 144 square meters ### Answer: 144 square meters
Expected answer: 144
Correct? Yes
Problem: A rectangle has a length of 13m and a width of 43m. What is the area of the rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the rectangle is 13m * 43m = <<13*43=559>>559 square meters. ### Answer: 559
Expected answer: 559
Correct? Yes
Problem: Suppose we realized later that the width of the rectangle was actually 42m, not 43m. What would then be the area of the rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the rectangle is 13m * 42m = <<13*42=546>>546 square meters. ### Answer: 546
Expected answer: 546
Correct? Yes
Problem: A rectangle has a width of 27m and a length of 47m. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter can be calculated as 2*(length + width). Perimeter = 2*(47m + 27m) = 2*(74m) = <<2*74=148>>148m ### Answer: 148m
Expected answer: 148
Correct? Yes
Problem: Suppose the width of the rectangle is actually 9m instead of 27m. What would be the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter can be calculated as 2*(length + width). Perimeter = 2*(47m + 9m) = 2*(56m) = <<2*56=112>>112m ### Answer: 112m
Expected answer: 112
Correct? Yes
Problem: A rectangular football field has an area of 21m * 42m, calculate the area of the football field.
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length * width Area = 21m * 42m Area = 882m^2 ### Answer: 882m^2
Expected answer: 882
Correct? Yes
Problem: A rectangle's area is found by multiplying its length by its width. If the width of a certain rectangle is 27m and the length is 25m, what is the area of the rectangle?
Qwen2-Math 72B:
Reasoning: The area of the rectangle is 27m * 25m = <<27*25=675>>675 square meters. ### Answer: 675
Expected answer: 675
Correct? Yes
Problem: Suppose the width of the rectangle in the previous problem was not 27m, but was instead 11m, with the length remaining at 25m. What would then be the new area of the rectangle?
Qwen2-Math 72B:
Reasoning: The new area of the rectangle is 11m * 25m = <<11*25=275>>275 square meters. ### Answer: 275
Expected answer: 275
Correct? Yes
Problem: A rectangle has a length of 45m and a width of 48m. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 * (length + width) = 2 * (45m + 48m) = 2 * 93m = 186m ### Answer: 186m
Expected answer: 186
Correct? Yes
Problem: In the previous example, consider if the width of the rectangle was actually 34m instead of 48m. Now, what would be the perimeter of that rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 * (length + width) = 2 * (45m + 34m) = 2 * 79m = 158m ### Answer: 158m
Expected answer: 158
Correct? Yes
Problem: A rectangle has a length of 11 meters and a width of 7 meters. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 x (length + width) = 2 x (11 + 7) = 2 x 18 = 36 meters. ### Answer: 36
Expected answer: 36
Correct? Yes
Problem: Suppose the length of the rectangle was instead 10 meters while the width remained 7 meters. What would be the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 x (length + width) = 2 x (10 + 7) = 2 x 17 = 34 meters. ### Answer: 34
Expected answer: 34
Correct? Yes
Problem: A rectangular field has a length of 30m and a width of 2m. Can you calculate the perimeter of the field?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two pairs of equal sides, the formula for the perimeter is P = 2*(length + width). Substituting the given values, we get P = 2*(30m + 2m) = 2*(32m) = 64m. ### Answer: 64m
Expected answer: 64
Correct? Yes
Problem: As a follow-up to the previous problem, let's say that the length of the rectangular field is reduced to 20m instead of 30m, while the width remains the same. What would the new perimeter of the field be?
Qwen2-Math 72B:
Reasoning: Using the same formula for the perimeter of a rectangle, P = 2*(length + width), we can substitute the new length and the same width to find the new perimeter. Substituting the new values, we get P = 2*(20m + 2m) = 2*(22m) = 44m. ### Answer: 44m
Expected answer: 44
Correct? Yes
Problem: A rectangle has one side that is 7m long and another side that is 8m long. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all four sides. The perimeter of the rectangle is 2*(7m+8m) = <<2*(7+8)=30>>30m. ### Answer: 30m
Expected answer: 30
Correct? Yes
Problem: Consider that the length of the rectangle was originally 19m instead of 7m. How would the new perimeter be calculated then?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all four sides. The new perimeter of the rectangle is 2*(19m+8m) = <<2*(19+8)=54>>54m. ### Answer: 54m
Expected answer: 54
Correct? Yes
Problem: A rectangle has a length of 14m and a width of 18m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. So, the perimeter is 14+18+14+18 = <<14+18+14+18=64>>64m. ### Answer: 64
Expected answer: 64
Correct? Yes
Problem: Now let's consider another rectangle. The length of this rectangle is 9m rather than 14m, while the width remains the same at 18m. What is the perimeter of this new rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. So, the perimeter is 9+18+9+18 = <<9+18+9+18=54>>54m. ### Answer: 54
Expected answer: 54
Correct? Yes
Problem: A rectangle has a length of 43 units and a width of 3 units. Calculate the perimeter of this rectangle.
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter can be calculated as 2*(length + width). Perimeter = 2*(43 + 3) = 2*46 = 92 units. ### Answer: 92
Expected answer: 92
Correct? Yes
Problem: Let's consider the same rectangle from before, but this time, the width has increased to 39 units while the length remained the same at 43 units. What is the new perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter can be calculated as 2*(length + width). Perimeter = 2*(43 + 39) = 2*82 = 164 units. ### Answer: 164
Expected answer: 164
Correct? Yes
Problem: A rectangle has one side that measures 36 meters and another side that measures 42 meters. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all four sides. The perimeter of this rectangle is 36+36+42+42 = <<36+36+42+42=156>>156 meters. ### Answer: 156
Expected answer: 156
Correct? Yes
Problem: Now suppose that the longer side of the rectangle measures 48 meters instead of 42. What would be the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all four sides. The new perimeter of this rectangle is 36+36+48+48 = <<36+36+48+48=168>>168 meters. ### Answer: 168
Expected answer: 168
Correct? Yes
Problem: A rectangle has a length of 1m and a width of 6m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. For this rectangle, the perimeter is 2*(length + width) = 2*(1m + 6m) = 2*7m = <<2*7=14>>14m. ### Answer: 14m
Expected answer: 14
Correct? Yes
Problem: Now consider that the length of the rectangle has changed to 28m, while the width remains at 6m. What is the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: With the new length of 28m and the width of 6m, the perimeter is calculated as 2*(length + width) = 2*(28m + 6m) = 2*34m = <<2*34=68>>68m. ### Answer: 68m
Expected answer: 68
Correct? Yes
Problem: A rectangle has two sides measuring 45m and two sides measuring 8m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all its sides. The perimeter of this rectangle is 45+45+8+8 = <<45+45+8+8=106>>106m. ### Answer: 106
Expected answer: 106
Correct? Yes
Problem: A rectangular garden has a length of 25 meters and a width of 37 meters. What is the perimeter of the garden?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the formula for the perimeter is P = 2l + 2w, where l is the length and w is the width. In this case, the length of the garden is 25 meters and the width is 37 meters. So, the perimeter of the garden is P = 2(25) + 2(37) = 50 + 74 = <<50+74=124>>124 meters. ### Answer: 124
Expected answer: 124
Correct? Yes
Problem: Suppose we reduce the length of the garden from 25 meters to 16 meters, while the width remains unchanged at 37 meters. What would be the new perimeter of the garden?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the formula for the perimeter is P = 2l + 2w, where l is the length and w is the width. In this case, the length of the garden is 16 meters and the width is 37 meters. So, the perimeter of the garden is P = 2(16) + 2(37) = 32 + 74 = <<32+74=106>>106 meters. ### Answer: 106
Expected answer: 106
Correct? Yes
Problem: A rectangle has length 36m and width 3m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is given by the formula 2*(length + width). The perimeter of the rectangle is 2*(36+3) = <<2*(36+3)=78>>78m. ### Answer: 78
Expected answer: 78
Correct? Yes
Problem: Suppose we made a change to the rectangle from the previous problem. Instead of a length of 36m, we shortened it to only 1m. What would be the new perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of the new rectangle is given by the formula 2*(length + width). The perimeter of the new rectangle is 2*(1+3) = <<2*(1+3)=8>>8m. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: A rectangular garden has a length of 45 meters and a width of 50 meters. Calculate the perimeter of the garden.
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. For this garden, the perimeter is 2 * (length + width) = 2 * (45 + 50) = 2 * 95 = <<2*95=190>>190 meters. ### Answer: 190
Expected answer: 190
Correct? Yes
Problem: A rectangle has a length of 44m and a width of 34m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. So, the perimeter is 2*(length + width) = 2*(44+34) = <<2*(44+34)=156>>156m. ### Answer: 156
Expected answer: 156
Correct? Yes
Problem: Now suppose the width of the rectangle changes to 36m while the length remains the same at 44m. What would be the new perimeter of the rectangle in this case?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. So, the new perimeter is 2*(length + new width) = 2*(44+36) = <<2*(44+36)=160>>160m. ### Answer: 160
Expected answer: 160
Correct? Yes
Problem: A rectangle has a length of 42 m and a width of 29 m. Calculate the perimeter of the rectangle.
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. The perimeter of the rectangle is 2*(42+29) = <<2*(42+29)=142>>142 m. ### Answer: 142
Expected answer: 142
Correct? Yes
Problem: Suppose the width of the rectangle was actually 38 m instead of 29 m. What would then be the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. The new perimeter of the rectangle is 2*(42+38) = <<2*(42+38)=160>>160 m. ### Answer: 160
Expected answer: 160
Correct? Yes
Problem: A rectangle has a length of 44 meters and a width of 35 meters. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 x (length + width) Perimeter = 2 x (44 + 35) Perimeter = 2 x 79 Perimeter = 158 meters ### Answer: 158
Expected answer: 158
Correct? Yes
Problem: Consider the same rectangle from the previous problem, but now the width has changed to 43 meters while the length remains the same at 44 meters. What is the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 x (length + width) Perimeter = 2 x (44 + 43) Perimeter = 2 x 87 Perimeter = 174 meters ### Answer: 174
Expected answer: 174
Correct? Yes
Problem: A rectangle has a length of 44m and a width of 45m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. For this rectangle, the perimeter is 2*(length + width) = 2*(44m + 45m) = 2*89m = <<2*89=178>>178m. ### Answer: 178m
Expected answer: 178
Correct? Yes
Problem: The previous rectangle had its width increased from 45m to 48m while keeping the length the same. What is the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The new width is 48m, and the length remains 44m. The new perimeter is 2*(length + new width) = 2*(44m + 48m) = 2*92m = <<2*92=184>>184m. ### Answer: 184m
Expected answer: 184
Correct? Yes
Problem: A rectangle has a length of 3 meters and a width of 39 meters. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. For a rectangle with length L and width W, the perimeter P is given by P = 2L + 2W. Given L = 3 meters and W = 39 meters, the perimeter is P = 2(3) + 2(39) = 6 + 78 = <<6+78=84>>84 meters. ### Answer: 84 meters
Expected answer: 84
Correct? Yes
Problem: Suppose the length of the rectangle was actually 17 meters instead of 3 meters, keeping the width the same. What would be the new perimeter of the rectangle now?
Qwen2-Math 72B:
Reasoning: With the new length L = 17 meters and the width W = 39 meters, the new perimeter P is calculated as P = 2L + 2W = 2(17) + 2(39) = 34 + 78 = <<34+78=112>>112 meters. ### Answer: 112 meters
Expected answer: 112
Correct? Yes
Problem: A rectangular garden has sides that measure 32m and 12m. What is the perimeter of this garden?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. So, the perimeter of the garden is 32m + 12m + 32m + 12m = <<32+12+32+12=88>>88m. ### Answer: 88m
Expected answer: 88
Correct? Yes
Problem: A rectangular swimming pool has a length of 24 feet and a width of 6 feet. What is the perimeter of the swimming pool?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding up all its sides. Since a rectangle has two lengths and two widths, the formula for the perimeter is P = 2L + 2W, where L is the length and W is the width. In this case, the length of the swimming pool is 24 feet and the width is 6 feet. So, the perimeter is P = 2(24) + 2(6) = 48 + 12 = <<48+12=60>>60 feet. ### Answer: 60
Expected answer: 60
Correct? Yes
Problem: A rectangle has a length of 27m and a width of 21m. What is the area of this rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 27m x 21m Area = 567m^2 ### Answer: 567m^2
Expected answer: 567
Correct? Yes
Problem: In the previous problem, the rectangle had a length of 27m and a width of 21m. Now, consider that the width of the rectangle is instead 8m. What is the area of this rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 27m x 8m Area = 216m^2 ### Answer: 216m^2
Expected answer: 216
Correct? Yes
Problem: A rectangle has twice the length of a square. If the square's side is 49m, what is the length of the rectangle?
Qwen2-Math 72B:
Reasoning: The length of the rectangle is twice the side of the square, which is 2*49 = <<2*49=98>>98m. ### Answer: 98m
Expected answer: 98
Correct? Yes
Problem: In the previous problem, we found the length of the rectangle when the square's side was 49m. Now, consider a square with a side length of 18m. What would be the length of the rectangle if it's still twice the length of the square?
Qwen2-Math 72B:
Reasoning: The length of the rectangle is twice the side of the square, which is 2*18 = <<2*18=36>>36m. ### Answer: 36m
Expected answer: 36
Correct? Yes
Problem: A rectangle has a length of 50m and a width of 36m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 * (length + width) = 2 * (50m + 36m) = 2 * 86m = 172m ### Answer: 172m
Expected answer: 172
Correct? Yes
Problem: In our previous rectangle, if we now increase the width from 36m to 44m, while keeping the length the same, what will be the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The new perimeter of the rectangle can be calculated using the same formula as before, but with the new width. Perimeter = 2 * (length + width) = 2 * (50m + 44m) = 2 * 94m = 188m ### Answer: 188m
Expected answer: 188
Correct? Yes
Problem: A rectangle has a length of 8m and a width of 44m. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter can be calculated as 2*(length + width). Therefore, the perimeter of the rectangle is 2*(8m + 44m) = <<2*(8+44)=104>>104m. ### Answer: 104m
Expected answer: 104
Correct? Yes
Problem: Consider the same rectangle from the previous problem, but now its length increases to 40m, while the width remains the same at 44m. What is the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter can be calculated as 2*(length + width). Therefore, the new perimeter of the rectangle is 2*(40m + 44m) = <<2*(40+44)=168>>168m. ### Answer: 168m
Expected answer: 168
Correct? Yes
Problem: If a rectangle has a length of 47 feet and a width of 21 feet, what is the area of the rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 47 feet x 21 feet Area = 987 square feet ### Answer: 987 square feet
Expected answer: 987
Correct? Yes
Problem: Now, suppose we adjusted the measurements of the previous rectangle. If the length of the rectangle remained the same at 21 feet, but the width of the rectangle was reduced to 15 feet, what would the new area of the rectangle be?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 21 feet x 15 feet Area = 315 square feet ### Answer: 315 square feet
Expected answer: 315
Correct? Yes
Problem: A rectangle has a length of 19m and a breadth of 28m. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal breadths, the perimeter can be calculated as follows: Perimeter = 2 * (length + breadth) = 2 * (19m + 28m) = 2 * 47m = 94m ### Answer: 94m
Expected answer: 94
Correct? Yes
Problem: In the previous problem, what if the length of the rectangle was 27m instead of 19m while keeping the breadth the same? What would be the new perimeter?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal breadths, the perimeter can be calculated as follows: Perimeter = 2 * (length + breadth) = 2 * (27m + 28m) = 2 * 55m = 110m ### Answer: 110m
Expected answer: 110
Correct? Yes
Problem: One side of a rectangle is four times the length of the other side. If the longer side measures 39 meters, what is the area of the rectangle when the shorter side is 10 meters?
Qwen2-Math 72B:
Reasoning: The shorter side of the rectangle is 39/4 = <<39/4=9.75>>9.75 meters. The area of the rectangle is 39*10 = <<39*10=390>>390 square meters. ### Answer: 390
Expected answer: 390
Correct? Yes
Problem: Suppose we discovered an error in the original measurements of the rectangle. The longer side is actually 37 meters instead of 39 meters. With the shorter side still at 10 meters, what is the new area of the rectangle?
Qwen2-Math 72B:
Reasoning: The shorter side of the rectangle remains 10 meters. The area of the rectangle is now 37*10 = <<37*10=370>>370 square meters. ### Answer: 370
Expected answer: 370
Correct? Yes
Problem: A rectangle has identical sides, each measuring 19 meters. What is the total perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding up all its sides. Since all sides are identical and measure 19 meters, the perimeter is 19+19+19+19 = <<19+19+19+19=76>>76 meters. ### Answer: 76
Expected answer: 76
Correct? Yes
Problem: The rectangle mentioned in the previous problem has been resized. The new rectangle now has a length of 19 meters but a width of 6 meters. What is the new total perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding up all its sides. The new rectangle has a length of 19 meters and a width of 6 meters. Therefore, the perimeter is 19+19+6+6 = <<19+19+6+6=50>>50 meters. ### Answer: 50
Expected answer: 50
Correct? Yes
Problem: The area of a rectangle is given by the equation length * width. If the length is 9m and the width is 26m, what is the area of the rectangle?
Qwen2-Math 72B:
Reasoning: The area of the rectangle is 9m * 26m = <<9*26=234>>234 square meters. ### Answer: 234
Expected answer: 234
Correct? Yes
Problem: The rectangle now has a new dimension with its length increased to 47m while the width is still 9m. What is the new area of the rectangle?
Qwen2-Math 72B:
Reasoning: The new area of the rectangle is 47m * 9m = <<47*9=423>>423 square meters. ### Answer: 423
Expected answer: 423
Correct? Yes
Problem: A rectangle has one side measuring 19cm and another side measuring 7cm. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. Since a rectangle has two pairs of equal sides, the perimeter is 2 * (19cm + 7cm) = <<2*(19+7)=64>>64cm. ### Answer: 64cm
Expected answer: 52
Correct? No
Problem: A shutter is in the shape of a rectangle. Its length is 10m and its width is 6m. What is the total area of the shutter?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the shutter is 10m * 6m = <<10*6=60>>60 square meters. ### Answer: 60 square meters
Expected answer: 60
Correct? Yes
Problem: A rectangle has a length of 24 units and a width of 15 units. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding up all its sides. Since a rectangle has two lengths and two widths, the formula for the perimeter is P = 2l + 2w, where l is the length and w is the width. Substituting the given values, we get P = 2(24) + 2(15) = 48 + 30 = <<48+30=78>>78 units. ### Answer: 78
Expected answer: 78
Correct? Yes
Problem: Now, imagine the rectangle's width was reduced to 10 units, while the length remained 24 units. What would be the new perimeter of the rectangle under these conditions?
Qwen2-Math 72B:
Reasoning: Using the same formula for the perimeter of a rectangle, P = 2l + 2w, we substitute the new width value of 10 units and the unchanged length value of 24 units. Thus, the new perimeter is P = 2(24) + 2(10) = 48 + 20 = <<48+20=68>>68 units. ### Answer: 68
Expected answer: 68
Correct? Yes
Problem: If a rectangular plot of land has a length of 32m and a width of 27m, what is the area of the plot in square meters?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 32m x 27m Area = 864 square meters ### Answer: 864
Expected answer: 864
Correct? Yes
Problem: In the previous scenario, suppose the width of the rectangular plot of land was actually 18m rather than 27m. What would then be the area of the plot in square meters?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 32m x 18m Area = 576 square meters ### Answer: 576
Expected answer: 576
Correct? Yes
Problem: A rectangle has one side that measures 15m and another side that measures 10m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding up all its sides. Since a rectangle has two pairs of equal sides, the perimeter is 2*(15m + 10m) = <<2*(15+10)=50>>50m. ### Answer: 50m
Expected answer: 50
Correct? Yes
Problem: Now consider the rectangle has one side that measures 33m instead of 15m while the other side still measures 10m. What is the new perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding up all its sides. Since a rectangle has two pairs of equal sides, the perimeter is 2*(33m + 10m) = <<2*(33+10)=86>>86m. ### Answer: 86m
Expected answer: 86
Correct? Yes
Problem: A rectangle has a length of 44m and a width of 37m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. So, the perimeter is 2*(length + width) = 2*(44+37) = <<2*(44+37)=162>>162m. ### Answer: 162
Expected answer: 162
Correct? Yes
Problem: What would the perimeter of the rectangle be if the length was 25m instead of 44m but the width remained the same at 37m?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. So, the perimeter is 2*(length + width) = 2*(25+37) = <<2*(25+37)=124>>124m. ### Answer: 124
Expected answer: 124
Correct? Yes
Problem: A rectangle has length of 14 cm and width 8 cm. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. The formula for the perimeter of a rectangle is P = 2(l + w), where l is the length and w is the width. Given that the length is 14 cm and the width is 8 cm, we can substitute these values into the formula: P = 2(14 + 8) = 2(22) = <<2*22=44>>44 cm. ### Answer: 44 cm
Expected answer: 44
Correct? Yes
Problem: If the length of the rectangle remains 14 cm, but the width is increased to 18 cm, what would be the new perimeter of the rectangle now?
Qwen2-Math 72B:
Reasoning: Using the same formula for the perimeter of a rectangle, P = 2(l + w), we can substitute the new values: P = 2(14 + 18) = 2(32) = <<2*32=64>>64 cm. ### Answer: 64 cm
Expected answer: 64
Correct? Yes
Problem: A rectangle has a length of 26m and a width of 28m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. For this rectangle, the perimeter is 2*(26+28) = <<2*(26+28)=108>>108m. ### Answer: 108
Expected answer: 108
Correct? Yes
Problem: In the previous scenario, if the rectangle was actually a square with all sides measuring 26m, what would the new perimeter be?
Qwen2-Math 72B:
Reasoning: The perimeter of a square is calculated by multiplying the length of one side by 4. For this square, the perimeter is 4*26 = <<4*26=104>>104m. ### Answer: 104
Expected answer: 104
Correct? Yes
Problem: A rectangle has a length of 15m and a width of 37m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 * (length + width) = 2 * (15m + 37m) = 2 * 52m = 104m ### Answer: 104m
Expected answer: 104
Correct? Yes
Problem: The width of the rectangle mentioned in the previous problem is now changed to 19m, while the length is still 15m. What is the new perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 * (length + width) = 2 * (15m + 19m) = 2 * 34m = 68m ### Answer: 68m
Expected answer: 68
Correct? Yes
Problem: A rectangle has a length of 42m and a width of 40m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. So, the perimeter is 42+40+42+40 = <<42+40+42+40=164>>164m. ### Answer: 164
Expected answer: 164
Correct? Yes
Problem: The rectangle you were previously given now has a length of 42m and the width has been adjusted to 24m. What is the new perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. So, the new perimeter is 42+24+42+24 = <<42+24+42+24=132>>132m. ### Answer: 132
Expected answer: 132
Correct? Yes
Problem: A rectangular garden has one side that measures 21 feet and another side that measures 30 feet. What is the perimeter of the garden?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter can be calculated as 2*(length + width). The perimeter of the garden is 2*(21+30) = <<2*(21+30)=102>>102 feet. ### Answer: 102
Expected answer: 102
Correct? Yes
Problem: Now, imagine that the side of the garden that initially measured 30 feet was actually only 5 feet long. What would be the new perimeter of the garden?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter can be calculated as 2*(length + width). The new perimeter of the garden is 2*(21+5) = <<2*(21+5)=52>>52 feet. ### Answer: 52
Expected answer: 52
Correct? Yes
Problem: A certain playground is in the shape of a rectangle. The area of the playground is given as the product of 17 and 44. How many square meters is the playground?
Qwen2-Math 72B:
Reasoning: The area of the playground is 17*44 = <<17*44=748>>748 square meters. ### Answer: 748
Expected answer: 748
Correct? Yes
Problem: Let's assume that the length of the playground was mistakenly recorded. Instead of 44m, the correct measurement is 37m. Given this information, how many square meters is the playground now?
Qwen2-Math 72B:
Reasoning: The area of the playground is now 17*37 = <<17*37=629>>629 square meters. ### Answer: 629
Expected answer: 629
Correct? Yes
Problem: Rectangle ABCD has a width of 47m and a length of 50m. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. The perimeter of rectangle ABCD is 2*(length + width) = 2*(50m + 47m) = 2*97m = <<2*97=194>>194m. ### Answer: 194m
Expected answer: 194
Correct? Yes
Problem: Now consider that the rectangle ABCD's dimensions have changed slightly. The width is still 47m, but the length has adjusted to 48m. What is the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. The perimeter of rectangle ABCD is 2*(length + width) = 2*(48m + 47m) = 2*95m = <<2*95=190>>190m. ### Answer: 190m
Expected answer: 190
Correct? Yes
Problem: A rectangle has a length of 11m and a width of 31m. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter can be calculated as 2*(length + width). Therefore, the perimeter of the rectangle is 2*(11m + 31m) = 2*42m = 84m. ### Answer: 84m
Expected answer: 84
Correct? Yes
Problem: Suppose we later find out that the actual length of the rectangle is 36m, not 11m as we originally thought, while the width remains the same at 31m. What would then be the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter can be calculated as 2*(length + width). Therefore, the new perimeter of the rectangle is 2*(36m + 31m) = 2*67m = 134m. ### Answer: 134m
Expected answer: 134
Correct? Yes
Problem: A rectangular garden has a length of 39m and a width of 19m. What is the area of this garden?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width = 39m x 19m = <<39*19=741>>741 square meters. ### Answer: 741
Expected answer: 741
Correct? Yes
Problem: If the length of the rectangular garden was actually 35m instead of 39m, keeping the width the same, what would be the new area of the garden?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width = 35m x 19m = <<35*19=665>>665 square meters. ### Answer: 665
Expected answer: 665
Correct? Yes
Problem: A carpenter wants to install a wooden floor in a rectangular hallway. The wooden plank has a width of 29 cm and the carpenter has cut it to a length of 11 cm. How many square centimeters of area does one cut wooden plank cover?
Qwen2-Math 72B:
Reasoning: The area of the wooden plank is 29*11 = <<29*11=319>>319 square centimeters. ### Answer: 319
Expected answer: 319
Correct? Yes
Problem: If instead the carpenter decided to cut the same 29 cm wide wooden plank into shorter lengths of 5 cm each, how many square centimeters of area does one of these shorter cut wooden planks cover?
Qwen2-Math 72B:
Reasoning: The area of the shorter wooden plank is 29*5 = <<29*5=145>>145 square centimeters. ### Answer: 145
Expected answer: 145
Correct? Yes
Problem: A rectangle has a length of 25m and a width of 11m. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the formula for the perimeter is P = 2l + 2w, where l is the length and w is the width. In this case, the length is 25m and the width is 11m. Plugging these values into the formula, we get: P = 2(25) + 2(11) P = 50 + 22 P = 72 Therefore, the perimeter of the rectangle is 72 meters. ### Answer: 72
Expected answer: 72
Correct? Yes
Problem: Now, suppose the rectangle's width is changed from 11m to 17m. What will be the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the formula for the perimeter is P = 2l + 2w, where l is the length and w is the width. In this case, the length is 25m and the width is 17m. Plugging these values into the formula, we get: P = 2(25) + 2(17) P = 50 + 34 P = 84 Therefore, the perimeter of the rectangle is 84 meters. ### Answer: 84
Expected answer: 84
Correct? Yes
Problem: A rectangle has a length of 49m and a breadth of 9m. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal breadths, the perimeter can be calculated as 2*(length + breadth). Perimeter = 2*(49m + 9m) = 2*(58m) = <<2*58=116>>116m ### Answer: 116m
Expected answer: 116
Correct? Yes
Problem: Suppose that the breadth of the same rectangle was instead 19m, while the length remains the same at 49m. What would be the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal breadths, the perimeter can be calculated as 2*(length + breadth). Perimeter = 2*(49m + 19m) = 2*(68m) = <<2*68=136>>136m ### Answer: 136m
Expected answer: 136
Correct? Yes
Problem: A rectangle has a length of 16m and a width of 7m. What is the area of this rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width = 16m x 7m = <<16*7=112>>112 square meters. ### Answer: 112
Expected answer: 112
Correct? Yes
Problem: The perimeter of a rectangular playground is found by the formula 2*(Length + Breadth). If the length of the playground is 14m and the breadth is 2m, what is the perimeter of the playground?
Qwen2-Math 72B:
Reasoning: The perimeter of the rectangular playground is 2*(14+2) = <<2*(14+2)=32>>32m. ### Answer: 32
Expected answer: 32
Correct? Yes
Problem: Now, consider that the breadth of the rectangular playground is changed to 3m, keeping the length the same as before (14m). What is the new perimeter of the playground?
Qwen2-Math 72B:
Reasoning: The new perimeter of the rectangular playground is 2*(14+3) = <<2*(14+3)=34>>34m. ### Answer: 34
Expected answer: 34
Correct? Yes
Problem: A square has a side length of 16 units. What is the perimeter of the square?
Qwen2-Math 72B:
Reasoning: The perimeter of a square is 4 times the side length. The perimeter of the square is 4*16 = <<4*16=64>>64 units. ### Answer: 64
Expected answer: 64
Correct? Yes
Problem: In the previous problem, the square's side length was 16 units. Now consider a rectangle with a length of 22 units and a width of 16 units. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is 2 times the length plus 2 times the width. The perimeter of the rectangle is 2*22+2*16 = <<2*22+2*16=76>>76 units. ### Answer: 76
Expected answer: 76
Correct? Yes
Problem: A rectangular garden has a width of 7 meters and a length of 21 meters. What is the perimeter of this garden?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. For this garden, the perimeter is 2*(7+21) = <<2*(7+21)=56>>56 meters. ### Answer: 56
Expected answer: 56
Correct? Yes
Problem: The width of the garden remains the same, but the length is reduced to 17 meters. Now, what is the new perimeter of the garden?
Qwen2-Math 72B:
Reasoning: With the new length, the perimeter is now calculated as 2*(7+17) = <<2*(7+17)=48>>48 meters. ### Answer: 48
Expected answer: 48
Correct? Yes
Problem: A rectangle has a length of 20 meters and a width of 5 meters. What is the area of the rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length × width Area = 20 meters × 5 meters Area = 100 square meters ### Answer: 100 square meters
Expected answer: 100
Correct? Yes
Problem: In the previous problem, we calculated the area of a rectangle with a length of 20 meters and a width of 5 meters. This time, instead of having the width as 5 meters, we have a new rectangle where the width is 17 meters. With the length still being 20 meters, what is the area of this new rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length × width Area = 20 meters × 17 meters Area = 340 square meters ### Answer: 340 square meters
Expected answer: 340
Correct? Yes
Problem: A rectangle has a length of 37m and a width of 43m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as 2*(length + width). Therefore, the perimeter of this rectangle is 2*(37m + 43m) = <<2*(37+43)=160>>160m. ### Answer: 160m
Expected answer: 160
Correct? Yes
Problem: Suppose the length of the rectangle is now changed to 32m while the width remains the same at 43m. What will be the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as 2*(length + width). Therefore, the new perimeter of this rectangle is 2*(32m + 43m) = <<2*(32+43)=150>>150m. ### Answer: 150m
Expected answer: 150
Correct? Yes
Problem: A rectangle has a length of 9m. If the width of the rectangle is 1m, what is the area?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 9m x 1m Area = 9m² ### Answer: 9m²
Expected answer: 9
Correct? Yes
Problem: In the previous problem, we considered a rectangle with a length of 9m and a width of 1m. Now, consider if the width of the rectangle was actually 40m instead of 1m. What would be the new area of the rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 9m x 40m Area = 360m² ### Answer: 360m²
Expected answer: 360
Correct? Yes
Problem: A rectangle's area is the product of 22m and 23m. What is the area of the rectangle?
Qwen2-Math 72B:
Reasoning: The area of the rectangle is 22m * 23m = <<22*23=506>>506 square meters. ### Answer: 506
Expected answer: 506
Correct? Yes
Problem: What if we reconsider the area of the rectangle, but this time its width is 6m instead of 23m, while maintaining the length at 22m. What would then be the area of the rectangle?
Qwen2-Math 72B:
Reasoning: The area of the rectangle is 22m * 6m = <<22*6=132>>132 square meters. ### Answer: 132
Expected answer: 132
Correct? Yes
Problem: A rectangle has one side that measures 14 cm and another side that measures 21 cm. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter can be calculated as 2*(length + width). In this case, the length is 21 cm and the width is 14 cm. Therefore, the perimeter is 2*(21 + 14) = 2*35 = 70 cm. ### Answer: 70 cm
Expected answer: 70
Correct? Yes
Problem: Consider the previous rectangle and suppose its side that previously measured 21 cm now measures 47 cm. What is the new perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter can be calculated as 2*(length + width). In this case, the length is 47 cm and the width is 14 cm. Therefore, the perimeter is 2*(47 + 14) = 2*61 = 122 cm. ### Answer: 122 cm
Expected answer: 122
Correct? Yes
Problem: In Clara's backyard, there is a rectangular swimming pool. The length of the pool is 23 meters, while the width is 12 meters. What is the area of the swimming pool in Clara's backyard?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = Length x Width Area = 23 meters x 12 meters Area = <<23*12=276>>276 square meters ### Answer: 276 square meters
Expected answer: 276
Correct? Yes
Problem: A rectangle has a length of 39 meters and a width of 8 meters. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 * (length + width) Perimeter = 2 * (39 + 8) Perimeter = 2 * 47 Perimeter = 94 meters ### Answer: 94
Expected answer: 94
Correct? Yes
Problem: Suppose the width of the rectangle was actually 23 meters instead of 8 meters. What would the perimeter of the rectangle be in this case?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 * (length + width) Perimeter = 2 * (39 + 23) Perimeter = 2 * 62 Perimeter = 124 meters ### Answer: 124
Expected answer: 124
Correct? Yes
Problem: A rectangle has a width of 27m and a length of 40m. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 * (length + width) Perimeter = 2 * (40m + 27m) Perimeter = 2 * 67m Perimeter = 134m ### Answer: 134m
Expected answer: 134
Correct? Yes
Problem: What if the length of the rectangle was 44m instead of 40m while keeping the width still at 27m? What would the new perimeter of the rectangle be?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 * (length + width) Perimeter = 2 * (44m + 27m) Perimeter = 2 * 71m Perimeter = 142m ### Answer: 142m
Expected answer: 142
Correct? Yes
Problem: A rectangle's length is 35m and its width is 9m. What is the perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as 2*(length + width). Therefore, the perimeter of the rectangle is 2*(35m + 9m) = <<2*(35+9)=88>>88m. ### Answer: 88m
Expected answer: 88
Correct? Yes
Problem: Suppose we resized the rectangle and shortened its length from 35m to 19m, while keeping the width the same. What would the new perimeter of the rectangle be?
Qwen2-Math 72B:
Reasoning: The new perimeter of the rectangle can be calculated using the same formula as before, but with the new length of 19m. Therefore, the new perimeter of the rectangle is 2*(19m + 9m) = <<2*(19+9)=56>>56m. ### Answer: 56m
Expected answer: 56
Correct? Yes
Problem: A rectangle has a length of 38m and a width of 11m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 * (length + width) = 2 * (38m + 11m) = 2 * 49m = 98m ### Answer: 98m
Expected answer: 98
Correct? Yes
Problem: In the rectangle mentioned earlier, suppose we now construct another rectangle such that its length remains the same (38m), but the width is now 23m instead of 11m. How would the perimeter of this new rectangle be calculated?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 * (length + width) = 2 * (38m + 23m) = 2 * 61m = 122m ### Answer: 122m
Expected answer: 122
Correct? Yes
Problem: One side of a rectangle is 28m long, and the other side is 29m long. What is the area of this rectangle?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 28m x 29m Area = 812 square meters ### Answer: 812 square meters
Expected answer: 812
Correct? Yes
Problem: Suppose the side of the rectangle previously mentioned gets extended to 35m instead of 29m, while the other side remains 28m. What would be the new area of the rectangle in this case?
Qwen2-Math 72B:
Reasoning: The area of a rectangle is calculated by multiplying its length by its width. Area = length x width Area = 28m x 35m Area = 980 square meters ### Answer: 980 square meters
Expected answer: 980
Correct? Yes
Problem: A square has a side length of 9m. What is the total length of fencing needed to enclose the square's perimeter?
Qwen2-Math 72B:
Reasoning: The perimeter of a square is 4 times the length of its side. The total length of fencing needed to enclose the square's perimeter is 4*9 = <<4*9=36>>36m. ### Answer: 36m
Expected answer: 36
Correct? Yes
Problem: A rectangle has a length of 38m and a width of 29m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 * (length + width) = 2 * (38m + 29m) = 2 * 67m = 134m ### Answer: 134m
Expected answer: 134
Correct? Yes
Problem: Now consider that the rectangle from the previous question actually had a length of 6m instead of 38m. What would be the new perimeter of the rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two equal lengths and two equal widths, the perimeter can be calculated as follows: Perimeter = 2 * (length + width) = 2 * (6m + 29m) = 2 * 35m = 70m ### Answer: 70m
Expected answer: 70
Correct? Yes
Problem: A rectangle has one side of length 45m and another side of length 47m. Find the perimeter of the rectangle.
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. Since a rectangle has two pairs of equal sides, the perimeter is 2*(45+47) = <<2*(45+47)=184>>184m. ### Answer: 184
Expected answer: 184
Correct? Yes
Problem: Suppose the length of one side of the rectangle is altered from 47m to 46m. What would be the new perimeter of the rectangle now?
Qwen2-Math 72B:
Reasoning: The new perimeter of the rectangle would be 2*(45+46) = <<2*(45+46)=182>>182m. ### Answer: 182
Expected answer: 182
Correct? Yes
Problem: Given a rectangle where the length is 24m and the width is 20m, what is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated as 2*(length + width). So, the perimeter of this rectangle is 2*(24+20) = <<2*(24+20)=96>>96m. ### Answer: 96
Expected answer: 88
Correct? No
Problem: The length and width of a rectangle are both 32m. What is the perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. Since the length and width are both 32m, the perimeter is 2*(32+32) = <<2*(32+32)=128>>128m. ### Answer: 128m
Expected answer: 128
Correct? Yes
Problem: The length of the rectangle from the previous problem remains the same, but the width of the rectangle is now adjusted to 13m. What is the new perimeter of this rectangle?
Qwen2-Math 72B:
Reasoning: The perimeter of a rectangle is calculated by adding all its sides. Since the length is 32m and the width is now 13m, the perimeter is 2*(32+13) = <<2*(32+13)=88>>88m. ### Answer: 88m
Expected answer: 90
Correct? No