Gemma 2B 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(21m + 37m) = 2(58m) = 116m. ### Answer: 116
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(4m + 37m) = 2(41m) = 82m. ### Answer: 82
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(50 + 20) = 2(70) = <<2(70)=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?
Gemma 2B:
Reasoning: The new perimeter will be given by the formula P = 2(length + width). Substituting the values, we get P = 2(15 + 20) = 2(35) = <<2(35)=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?
Gemma 2B:
Reasoning: The area of a rectangle is equal to the length times the width, which is 26m x 7m = <<26m x 7m=182m²>>182 square meters. ### Answer: 182
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?
Gemma 2B:
### Answer: 35m x 7m = 240m²
Expected answer: 245
Correct? No
Problem: A rectangle has a length of 50m and a width of 15m. What is its perimeter?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(50 + 15) = 2(65) = 130m. ### Answer: 130
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(50 + 9) = 2(59) = 118m. ### Answer: 118
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)?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by P = 2(length + width). Substituting the values, we get P = 2(5m + 19m) = 2(24m) = 48m. Therefore, the total distance around the fence is 48m.
Expected answer: 48
Correct? Yes
Problem: A rectangle has sides of length 49m and 6m. What is the perimeter of the rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(49m + 6m) = 2(55m) = 110m. ### Answer: 110
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?
Gemma 2B:
Reasoning: If one side is 17m, the other side would be 49m - 17m = 32m. The perimeter would then be P = 2(49m + 32m) = 2(81m) = 162m. ### Answer: 162
Expected answer: 46
Correct? No
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by P = 2(length + width). In this case, the length is 26m and the width is 7m, so the perimeter is: P = 2(7m + 26m) = 2(33m) = 66m. Therefore, Joshua will need 66m of wire to enclose his garden completely.
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(18 m + 11 m) = 2(29 m) = 58 m. ### Answer: 58
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the new values, we get P = 2(18 m + 44 m) = 2(62 m) = 124 m. ### Answer: 124
Expected answer: 124
Correct? Yes
Problem: The dimensions of a rectangle are 22 feet by 39 feet. What is the perimeter of the rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(22 ft + 39 ft) = 2(61 ft) = 122 ft. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the new length and width, we get P = 2(26 ft + 22 ft) = 2(48 ft) = 96 ft. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(45 + 25) = 2(70) = <<2(70)=140>>140 cm. ### Answer: 140
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?
Gemma 2B:
Reasoning: The perimeter remains the same, as it is calculated based on the length and width of the rectangle. Therefore, the adjusted perimeter would be 2(45 + 42) = 2(87) = <<2(87)=174>>174 cm. ### Answer: 174
Expected answer: 134
Correct? No
Problem: A rectangular garden has a length of 8m and a width of 5m. What is the perimeter of this garden?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(8m + 5m) = 2(13m) = 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?
Gemma 2B:
Reasoning: The new length is 46m, and the width is still 5m. The new perimeter is given by the formula P = 2(length + width) = 2(46m + 5m) = 2(51m) = 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?
Gemma 2B:
Reasoning: The area of a rectangle is equal to the length times the width, which is 19 units x 17 units = <<19x17=313>>313 square units. ### Answer: 313
Expected answer: 323
Correct? No
Problem: A rectangle has a length of 42 meters and a width of 8 meters. What is the perimeter of the rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(42 + 8) = 2(50) = 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?
Gemma 2B:
Reasoning: The area of a rectangle is equal to the length times the width, which is 38m x 16m = <<38m x 16m=640>>640 square meters. ### Answer: 640
Expected answer: 608
Correct? No
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?
Gemma 2B:
Reasoning: The area of a rectangle is calculated by multiplying its length and width. Area = Length x Width = 28m x 17m = <<28m x 17m=476m^2>>476 square meters. ### Answer: 476
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?
Gemma 2B:
Reasoning: The area of a rectangle is calculated by multiplying its length and width. Area = Length x Width = 10m x 17m = <<10m x 17m=170m^2>>170 square meters. ### Answer: 170
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(43m + 41m) = 2(84m) = 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?
Gemma 2B:
Reasoning: The new length would be 18m, and the new width would be 41m. Substituting these values into the formula, we get P = 2(18m + 41m) = 2(69m) = 138m. ### Answer: 138
Expected answer: 118
Correct? No
Problem: A rectangle has one side that measures 44m, and the other side that measures 17m. What is the perimeter of the rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(44 + 17) = 2(61) = <<2(61)=122>>122m. ### Answer: 122
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(44 + 21) = 2(65) = <<2(65)=130>>130m. ### Answer: 130
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by P = 2(length + width). Substituting the values, we get P = 2(20m + 2m) = 2(22m) = 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?
Gemma 2B:
Reasoning: The new width is 32m, and the new length is 20m. Substituting these values into the formula, we get P = 2(20m + 32m) = 2(52m) = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(4 m + 5 m) = 2(9 m) = 18 m. ### 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?
Gemma 2B:
Reasoning: The perimeter remains the same as before, as it is calculated as 2(length + width). Substituting the new values, we get P = 2(42 m + 5 m) = 2(47 m) = 94 m. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(45m + 37m) = 2(82m) = 164m. ### Answer: 164
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(45m + 47m) = 2(92m) = 184m. ### Answer: 184
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(27m + 21m) = 2(48m) = 96m. ### Answer: 96
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?
Gemma 2B:
Reasoning: The new perimeter would be given by the formula P = 2(length + width) = 2(45m + 21m) = 2(66m) = 132m. ### Answer: 132
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(30m + 20m) = 2(50m) = 100m. ### Answer: 100
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the new values, we get P = 2(30m + 48m) = 2(78m) = 156m. ### Answer: 156
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(30m + 27m) = 2(57m) = 114m. ### Answer: 114
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?
Gemma 2B:
Reasoning: The area of a rectangle is calculated by multiplying its length and width. Area = Length x Width = 23m x 11m = <<23m x 11m=265m^2>>265m^2. ### Answer: 265
Expected answer: 253
Correct? No
Problem: A rectangle has a length of 3m and a width of 9m. What would be the total perimeter of this rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 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?
Gemma 2B:
Reasoning: The new perimeter is given by the formula P = 2(length + width). Substituting the values, we get P = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(31m + 6m) = 2(37m) = 74m. ### Answer: 74
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(43m + 6m) = 2(50m) = 100m. ### Answer: 100
Expected answer: 98
Correct? No
Problem: A rectangle has a length of 12m and a width of 33m. What is the area of this rectangle?
Gemma 2B:
Reasoning: The area of a rectangle is equal to the length times the width, so 12m * 33m = <<12m*33m=396m²>>396m². ### Answer: 396
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?
Gemma 2B:
### Answer: 594
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(20m + 20m) = 2(40m) = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(35m + 9m) = 2(44m) = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(26m + 9m) = 2(35m) = 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?
Gemma 2B:
Reasoning: The area of a rectangle is equal to the length times the width, so 9m * 25m = <<9m*25m=225m²>>225m². ### Answer: 225
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?
Gemma 2B:
Reasoning: The area of a rectangle is equal to the length times the width, so 16m * 9m = <<16m*9m=144m²>>144m². ### Answer: 144
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?
Gemma 2B:
Reasoning: The area of a rectangle is equal to the length times the width, so 13m * 43m = <<13m*43m=529m^2>>529m^2. ### Answer: 529m^2
Expected answer: 559
Correct? No
Problem: A rectangle has a width of 27m and a length of 47m. What is the perimeter of the rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(47m + 27m) = 2(74m) = <<2(74m)=148m>>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?
Gemma 2B:
Reasoning: If the width is changed to 9m, the length would remain the same at 47m. Therefore, the new perimeter would be P = 2(47m + 9m) = 2(56m) = <<2(56m)=112m>>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.
Gemma 2B:
Reasoning: The area of a rectangle is equal to the length times the width, so 21m * 42m = <<21m*42m=884m2>>884 square meters. ### Answer: 884
Expected answer: 882
Correct? No
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?
Gemma 2B:
Reasoning: The area of a rectangle is A = L x W, where A is the area, L is the length, and W is the width. Substituting the values, we get A = 25m x 27m = <<25m x 27m=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?
Gemma 2B:
Reasoning: The area of a rectangle is A = L x W, where A is the area, L is the length, and W is the width. Substituting the values, we get A = 25m x 11m = <<25m x 11m=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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(45m + 48m) = 2(93m) = 186m. ### Answer: 186
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?
Gemma 2B:
### Answer: 140m
Expected answer: 158
Correct? No
Problem: A rectangle has a length of 11 meters and a width of 7 meters. What is the perimeter of the rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(11 m + 7 m) = 2(18 m) = 36 m. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(10 m + 7 m) = 2(17 m) = 34 m. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(30m + 2m) = 2(32m) = 64m. ### Answer: 64
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?
Gemma 2B:
Reasoning: The new perimeter will be calculated using the same formula: P = 2(length + width). Substituting the new values, we get P = 2(20m + 2m) = 2(22m) = 44m. ### Answer: 44
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(7m + 8m) = 2(15m) = 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?
Gemma 2B:
### Answer: 34m
Expected answer: 54
Correct? No
Problem: A rectangle has a length of 14m and a width of 18m. What is the perimeter of this rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(14m + 18m) = 2(22m) = 44m. ### Answer: 44m
Expected answer: 64
Correct? No
Problem: A rectangle has a length of 43 units and a width of 3 units. Calculate the perimeter of this rectangle.
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values of the sides, we get P = 2(36 + 42) = 2(78) = <<2(78)=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?
Gemma 2B:
Reasoning: If the longer side is 48 meters, the shorter side will be 42 meters. Therefore, the new perimeter would be P = 2(48 + 42) = 2(90) = <<2(90)=180>>180 meters. ### Answer: 180
Expected answer: 168
Correct? No
Problem: A rectangle has a length of 1m and a width of 6m. What is the perimeter of this rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(1m + 6m) = 2(7m) = <<2(7m)=14m>>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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the new values, we get P = 2(28m + 6m) = 2(34m) = <<2(34m)=70m>>70m. ### Answer: 70m
Expected answer: 68
Correct? No
Problem: A rectangle has two sides measuring 45m and two sides measuring 8m. What is the perimeter of this rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(45 + 8) = 2(53) = <<2(53)=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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(25 m + 37 m) = 2(62 m) = 124 m. ### 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?
Gemma 2B:
Reasoning: The new length is 16 m, and the new width is 37 m. Substituting these values into the formula, we get P = 2(16 m + 37 m) = 2(53 m) = 106 m. ### Answer: 106
Expected answer: 106
Correct? Yes
Problem: A rectangle has length 36m and width 3m. What is the perimeter of this rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(36m + 3m) = 2(40m) = 80m. ### Answer: 80
Expected answer: 78
Correct? No
Problem: A rectangular garden has a length of 45 meters and a width of 50 meters. Calculate the perimeter of the garden.
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(45 + 50) = 2(95) = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(44m + 34m) = 2(78m) = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is independent of the width, so the new perimeter will still be 156m. ### Answer: 156
Expected answer: 160
Correct? No
Problem: A rectangle has a length of 42 m and a width of 29 m. Calculate the perimeter of the rectangle.
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(42 m + 29 m) = 2(71 m) = 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?
Gemma 2B:
Reasoning: If the width was 38 m, the length would be 42 m (as given). Therefore, the new perimeter would be P = 2(42 m + 38 m) = 2(80 m) = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(44 + 35) = 2(79) = <<2(79)=158>>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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(44 + 43) = 2(87) = <<2(87)=174>>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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(44m + 45m) = 2(89m) = 178m. ### Answer: 178
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(44m + 48m) = 2(92m) = 184m. ### Answer: 184
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(3 + 39) = 2(42) = <<2(42)=84>>84 meters. ### Answer: 84
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the new length, we get P = 2(17 + 3) = 2(20) = <<2(20)=40>>40 meters. ### Answer: 40
Expected answer: 112
Correct? No
Problem: A rectangular garden has sides that measure 32m and 12m. What is the perimeter of this garden?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values of the sides, we get P = 2(32m + 12m) = 2(44m) = 88m. ### Answer: 88
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(24 + 6) = 2(30) = 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?
Gemma 2B:
Reasoning: The area of a rectangle is calculated by multiplying its length and width. Area = Length x Width = 27m x 21m = <<27m x 21m=567m^2>>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?
Gemma 2B:
Reasoning: The area of a rectangle is calculated by multiplying its length and width. Area = Length x Width = 27m x 8m = <<27m x 8m=232m^2>>232m^2. ### Answer: 232m^2
Expected answer: 216
Correct? No
Problem: A rectangle has twice the length of a square. If the square's side is 49m, what is the length of the rectangle?
Gemma 2B:
Reasoning: Let x be the side of the square. Then, the length of the rectangle is 2x. The area of the square is x^2. The area of the rectangle is 2x^2. Since the rectangle has twice the length of the square, we have 2x = x^2. Solving for x, we get x = 7. Therefore, the side of the square is 49m, and the length of the rectangle is 2 * 49 = 98m.
Expected answer: 98
Correct? Yes
Problem: A rectangle has a length of 50m and a width of 36m. What is the perimeter of this rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(50m + 36m) = 2(86m) = 172m. ### Answer: 172
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the new width as 44m and the same length as 50m, we get P = 2(50m + 44m) = 2(94m) = 188m. ### Answer: 188
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(8m + 44m) = 2(52m) = 104m. ### Answer: 104
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the new values, we get P = 2(40m + 44m) = 2(84m) = 168m. ### Answer: 168
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?
Gemma 2B:
Reasoning: The area of a rectangle is length times width, so 47 x 21 = <<47 x 21=977>>977 square feet. ### Answer: 977
Expected answer: 987
Correct? No
Problem: A rectangle has a length of 19m and a breadth of 28m. What is the perimeter of the rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + breadth). Substituting the values, we get P = 2(19m + 28m) = 2(47m) = 94m. ### Answer: 94
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?
Gemma 2B:
Reasoning: If the length of the rectangle was 27m, the perimeter would be P = 2(19m + 27m) = 2(46m) = 92m. ### Answer: 92
Expected answer: 110
Correct? No
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?
Gemma 2B:
Reasoning: The longer side is 4 times the shorter side, so 4x = 10. Solving for x, we get x = 2.5. The area of the rectangle is A = length * width = 4x * 10 = 40 square meters. ### Answer: 40
Expected answer: 390
Correct? No
Problem: A rectangle has identical sides, each measuring 19 meters. What is the total perimeter of the rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, the length and width are both 19 meters, so the perimeter is P = 2(19) = <<2(19)=38>>38 meters. ### Answer: 38
Expected answer: 76
Correct? No
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?
Gemma 2B:
Reasoning: The area of the rectangle is 9m * 26m = <<9m*26m=234m^2>>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?
Gemma 2B:
Reasoning: The new area of the rectangle is 47m * 9m = <<47m*9m=405m^2>>405 square meters. ### Answer: 405
Expected answer: 423
Correct? No
Problem: A rectangle has one side measuring 19cm and another side measuring 7cm. What is the perimeter of the rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(19 cm + 7 cm) = 2(26 cm) = 52 cm. ### Answer: 52
Expected answer: 52
Correct? Yes
Problem: Suppose we extended the rectangle's length from the previous question from 19cm to 21cm. In this case, what would be the new perimeter?
Gemma 2B:
Reasoning: The perimeter of a rectangle is independent of its length, only affected by its width. Therefore, the new perimeter would be 2(21 cm) = 42 cm. ### Answer: 42
Expected answer: 56
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?
Gemma 2B:
Reasoning: The total area of the shutter is equal to the length times the width, which is 10m x 6m = <<10m x 6m=60m²>>60 square meters. ### Answer: 60
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(24 units + 15 units) = 2(39 units) = 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?
Gemma 2B:
Reasoning: The new perimeter would be given by the formula P = 2(length + width). Substituting the values, we get P = 2(24 units + 10 units) = 2(34 units) = 78 units. ### Answer: 78
Expected answer: 68
Correct? No
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?
Gemma 2B:
Reasoning: The area of a rectangle is calculated by multiplying its length and width. The area of the plot = 32m * 27m = <<32m*27m=864m^2>>864 square meters.
Expected answer: 864
Correct? Yes
Problem: A rectangle has one side that measures 15m and another side that measures 10m. What is the perimeter of this rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(15m + 10m) = 2(25m) = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(33m + 10m) = 2(43m) = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(44m + 37m) = 2(81m) = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(25m + 37m) = 2(62m) = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(14 cm + 8 cm) = 2(22 cm) = 44 cm. ### Answer: 44
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(14 cm + 18 cm) = 2(32 cm) = 64 cm. ### Answer: 64
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(26m + 28m) = 2(54m) = 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?
Gemma 2B:
### Answer: 108m
Expected answer: 104
Correct? No
Problem: A rectangle has a length of 15m and a width of 37m. What is the perimeter of this rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(15m + 37m) = 2(52m) = 104m. ### Answer: 104
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the new values, we get P = 2(15m + 19m) = 2(34m) = 70m. ### Answer: 70
Expected answer: 68
Correct? No
Problem: A rectangle has a length of 42m and a width of 40m. What is the perimeter of this rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(42m + 40m) = 2(82m) = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(42m + 24m) = 2(66m) = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values of the sides, we get P = 2(21 + 30) = 2(51) = 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?
Gemma 2B:
Reasoning: If one side of the garden is only 5 feet long, then the other side must be 30 feet long. Therefore, the new perimeter would be P = 2(21 + 30) = 2(51) = 102 feet. ### Answer: 102
Expected answer: 52
Correct? No
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?
Gemma 2B:
Reasoning: The area of a rectangle is given as the product of its length and width. Therefore, 17 * 44 = <<17*44=744>>744 square meters. ### Answer: 744
Expected answer: 748
Correct? No
Problem: Rectangle ABCD has a width of 47m and a length of 50m. What is the perimeter of the rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(50m + 47m) = 2(97m) = 194m. ### Answer: 194
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is unchanged if the length and width are changed in the same ratio. Therefore, the new perimeter is also 194m. ### Answer: 194
Expected answer: 190
Correct? No
Problem: A rectangle has a length of 11m and a width of 31m. What is the perimeter of the rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(11m + 31m) = 2(42m) = 84m. ### Answer: 84
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?
Gemma 2B:
Reasoning: The perimeter remains the same as 2(length + width) = 2(36m + 31m) = 2(67m) = 134m. ### Answer: 134
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?
Gemma 2B:
Reasoning: The area of a rectangle is calculated by multiplying its length and width. Area = Length x Width = 39m x 19m = <<39m x 19m=729m^2>>729 square meters. ### Answer: 729
Expected answer: 741
Correct? No
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?
Gemma 2B:
Reasoning: The area of the wooden plank is equal to the product of its width and length: 29 cm * 11 cm = <<29 cm * 11 cm=329 cm^2>>329 square centimeters. ### Answer: 329
Expected answer: 319
Correct? No
Problem: A rectangle has a length of 25m and a width of 11m. What is the perimeter of the rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(25m + 11m) = 2(36m) = 72m. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is independent of the width, so the new perimeter will still be 72m. ### Answer: 72
Expected answer: 84
Correct? No
Problem: A rectangle has a length of 49m and a breadth of 9m. What is the perimeter of the rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + breadth). Substituting the values, we get P = 2(49m + 9m) = 2(58m) = 116m. ### Answer: 116
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + breadth). Substituting the values, we get P = 2(49m + 19m) = 2(68m) = 136m. ### Answer: 136
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?
Gemma 2B:
Reasoning: The area of a rectangle is equal to the length times the width, which is 16m x 7m = <<16m x 7m=112m²>>112m². ### 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?
Gemma 2B:
### Answer: 34m
Expected answer: 32
Correct? No
Problem: A square has a side length of 16 units. What is the perimeter of the square?
Gemma 2B:
Reasoning: The perimeter of a square is equal to 4 times the side length. So, the perimeter of the square is 4 * 16 = <<4 * 16=64>>64 units.
Expected answer: 64
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(21 m + 7 m) = 2(28 m) = 56 m. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(17 m + 7 m) = 2(24 m) = 48 m. ### 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?
Gemma 2B:
Reasoning: The area of a rectangle is equal to the length times the width, which is 20 * 5 = <<20*5=100>>100 square meters. ### Answer: 100
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?
Gemma 2B:
### Answer: 400
Expected answer: 340
Correct? No
Problem: A rectangle has a length of 37m and a width of 43m. What is the perimeter of this rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(37m + 43m) = 2(80m) = 160m. ### Answer: 160
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the new values, we get P = 2(32m + 43m) = 2(75m) = 150m. ### Answer: 150
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?
Gemma 2B:
Reasoning: The area of a rectangle is length times width, so 9m * 1m = <<9m*1m=9m>>9m. ### Answer: 9m
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?
Gemma 2B:
Reasoning: If the width was 40m, the area would be 9m * 40m = <<9m*40m=360m>>360m. ### Answer: 360m
Expected answer: 360
Correct? Yes
Problem: A rectangle's area is the product of 22m and 23m. What is the area of the rectangle?
Gemma 2B:
Reasoning: The area of the rectangle is 22m * 23m = <<22m*23m=520m^2>>520 square meters. ### Answer: 520
Expected answer: 506
Correct? No
Problem: A rectangle has one side that measures 14 cm and another side that measures 21 cm. What is the perimeter of this rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(14 cm + 21 cm) = 2(35 cm) = 70 cm. ### Answer: 70
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(47 cm + 21 cm) = 2(68 cm) = 136 cm. ### Answer: 136
Expected answer: 122
Correct? No
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?
Gemma 2B:
Reasoning: The area of a rectangle is calculated by multiplying its length and width. The area of the swimming pool is 23 * 12 = <<23*12=268>>268 square meters. ### Answer: 268
Expected answer: 276
Correct? No
Problem: A rectangle has a length of 39 meters and a width of 8 meters. What is the perimeter of this rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(39 m + 8 m) = 2(47 m) = 94 m. ### 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?
Gemma 2B:
Reasoning: If the width was 23 m, the length would be 39 m (as given). Substituting these values into the formula, we get P = 2(39 m + 23 m) = 2(62 m) = 124 m. ### 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(40m + 27m) = 2(67m) = 134m. ### Answer: 134
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?
Gemma 2B:
Reasoning: If the length was 44m, the perimeter would be P = 2(40m + 27m) = 2(67m) = 134m.
Expected answer: 142
Correct? No
Problem: A rectangle's length is 35m and its width is 9m. What is the perimeter of the rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(35m + 9m) = 2(44m) = 88m. ### Answer: 88
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is independent of its length, only affected by its width. Therefore, the new perimeter will be the same as the original perimeter, which is 88m. ### Answer: 88
Expected answer: 56
Correct? No
Problem: A rectangle has a length of 38m and a width of 11m. What is the perimeter of this rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(38m + 11m) = 2(49m) = 98m. ### Answer: 98
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?
Gemma 2B:
### Answer: 52m
Expected answer: 122
Correct? No
Problem: One side of a rectangle is 28m long, and the other side is 29m long. What is the area of this rectangle?
Gemma 2B:
Reasoning: The area of a rectangle is equal to the length times the width, so 28m * 29m = <<28m*29m=844>>844 square meters. ### Answer: 844
Expected answer: 812
Correct? No
Problem: A square has a side length of 9m. What is the total length of fencing needed to enclose the square's perimeter?
Gemma 2B:
Reasoning: The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the side length. Substituting the values, we get P = 4 * 9 = <<4 * 9=36>>36 meters. ### Answer: 36
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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(38m + 29m) = 2(67m) = 134m. ### Answer: 134
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?
Gemma 2B:
Reasoning: If the length is changed to 6m, the perimeter becomes P = 2(38m + 29m) = 2(67m) = 134m. ### Answer: 134
Expected answer: 70
Correct? No
Problem: A rectangle has one side of length 45m and another side of length 47m. Find the perimeter of the rectangle.
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(45m + 47m) = 2(92m) = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is independent of the length of one side, as it is determined by the length of both sides. Therefore, the new perimeter would be 2(45m + 46m) = 2(91m) = 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?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(24m + 20m) = 2(44m) = 88m. ### Answer: 88
Expected answer: 88
Correct? Yes
Problem: Continuing from the previous scenario, imagine the length of the rectangle stayed the same at 24m, but the width was reduced to 17m. Now, what would be the new perimeter of this rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(24m + 17m) = 2(41m) = 82m. ### Answer: 82
Expected answer: 82
Correct? Yes
Problem: The length and width of a rectangle are both 32m. What is the perimeter of this rectangle?
Gemma 2B:
Reasoning: The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values, we get P = 2(32) = 64m. ### Answer: 64
Expected answer: 128
Correct? No