LLemma 7B 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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The length of the rectangle is 21m. The width of the rectangle is 37m. The perimeter of the rectangle is 21+37 = <<21+37=58>>58m. ### Answer: 58
Expected answer: 116
Correct? No
Problem: A rectangular garden has a length of 50 feet and a width of 20 feet. What is the perimeter of the garden?
LLemma 7B:
The perimeter of a rectangle is the sum of its length and width. The perimeter of the garden is 50+20 = <<50+20=70>>70 feet. ### Answer: 70
Expected answer: 140
Correct? No
Problem: A rectangle has a width of 7m and a length of 26m. What is the area of this rectangle?
LLemma 7B:
Reasoning: The area of a rectangle is the product of its length and width. The area of this rectangle is 7 x 26 = <<7*26=182>>182 m^2. ### 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?
LLemma 7B:
Reasoning: The area of a rectangle is the product of its length and width. The area of the rectangle now is 7 x 35 = <<7*35=245>>245 m^2. ### Answer: 245
Expected answer: 245
Correct? Yes
Problem: A rectangle has a length of 50m and a width of 15m. What is its perimeter?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its length and width. The perimeter of the rectangle is 50+15 = <<50+15=65>>65m. ### Answer: 65
Expected answer: 130
Correct? No
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)?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The perimeter of the fence is 5+19=<<5+19=24>>24 meters. ### Answer: 24
Expected answer: 48
Correct? No
Problem: A rectangle has sides of length 49m and 6m. What is the perimeter of the rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The perimeter of the rectangle is 49+6+49+6 = <<49+6+49+6=104>>104m. ### Answer: 104
Expected answer: 110
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?
LLemma 7B:
Reasoning: The wire will be used to enclose the perimeter of the garden. The perimeter of a rectangle is 2(length + width). Joshua needs 2(7+26) = <<2(7+26)=68>>68 meters of wire. ### Answer: 68
Expected answer: 66
Correct? No
Problem: A rectangle has a length of 18 meters and a width of 11 meters. What is the perimeter of the rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The length of the rectangle is 18 meters. The width of the rectangle is 11 meters. The perimeter of the rectangle is 18+11 = <<18+11=29>>29 meters. ### Answer: 29
Expected answer: 58
Correct? No
Problem: The dimensions of a rectangle are 22 feet by 39 feet. What is the perimeter of the rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is 2(l+w) = <<2(22+39) = 2(61) = 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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is 2(l+w) = <<2(22+26) = 2(48) = 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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all its sides. The perimeter of the rectangle is 45+25+45+25 = <<45+25+45+25=150>>150m. ### Answer: 150
Expected answer: 140
Correct? No
Problem: A rectangular garden has a length of 8m and a width of 5m. What is the perimeter of this garden?
LLemma 7B:
The perimeter of a rectangle is the sum of its length and width. The perimeter of this garden is 8+5 = <<8+5=13>>13m. ### Answer: 13
Expected answer: 26
Correct? No
Problem: In a rectangle, the length is 19 units and the width is 17 units. What is the area of this rectangle?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of this rectangle is 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?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of this rectangle is 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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 42+8+42+8 = <<42+8+42+8=96>>96 meters. ### Answer: 96
Expected answer: 100
Correct? No
Problem: A rectangle has a width of 16m and a length of 38m. What is the area of this rectangle?
LLemma 7B:
Reasoning: The area of a rectangle is the product of its length and width. The area of this rectangle is 16 x 38 = <<16*38=576>>576 m^2. ### Answer: 576
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?
LLemma 7B:
Reasoning: The area of a rectangle is the product of its length and width. The area of the plot is 28 x 17 = <<28*17=476>>476 m^2. ### 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?
LLemma 7B:
Reasoning: The area of a rectangle is the product of its length and width. The area of the plot is 10 x 17 = <<10*17=170>>170 m^2. ### 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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle 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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 18+41+18+41 = <<18+41+18+41=108>>108m. ### Answer: 108
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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all the sides. The length of the rectangle is 44m. The width of the rectangle is 17m. The perimeter of the rectangle is 44+17 = <<44+17=61>>61m. ### Answer: 61
Expected answer: 122
Correct? No
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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is 2(l+w). The perimeter of the rectangle is 2(20+2) = <<2(20+2)=44>>44. ### 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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is 2(l+w). The perimeter of the rectangle is 2(20+32) = <<2(20+32)=84>>84. ### Answer: 84
Expected answer: 104
Correct? No
Problem: A rectangle has a length of 4 meters and a width of 5 meters. What is the perimeter of the rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 4+5+4+5 = <<4+5+4+5=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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 42+5+42+5 = <<42+5+42+5=90>>90 meters. ### Answer: 90
Expected answer: 94
Correct? No
Problem: A rectangle has a length of 45m and a width of 37m. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of all of its sides. The perimeter of this rectangle is 45+37+45+37 = <<45+37+45+37=179>>179m. ### Answer: 179
Expected answer: 164
Correct? No
Problem: A rectangle has a length of 27m and a width of 21m. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of all of its sides. The perimeter of this rectangle is 27+21+27+21 = <<27+21+27+21=105>>105m. ### Answer: 105
Expected answer: 96
Correct? No
Problem: A rectangular garden has a length of 30m and a width of 20m. What is the perimeter of the garden?
LLemma 7B:
The perimeter of a rectangle is the sum of its length and width. The perimeter of the garden is 30+20 = <<30+20=50>>50m. ### Answer: 50
Expected answer: 100
Correct? No
Problem: A rectangle has a length of 30m and a width of 27m. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of all of its sides. The perimeter of this rectangle is 30+27+30+27 = <<30+27+30+27=124>>124m. ### Answer: 124
Expected answer: 114
Correct? No
Problem: A rectangle has a length of 23m and a width of 11m. What is the area of this rectangle?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of this rectangle is 23m x 11m = <<23*11=253>>253m^2. ### Answer: 253
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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of all of its sides. The length of the rectangle is 3m. The width of the rectangle is 9m. The perimeter of the rectangle is 3+3+9+9 = <<3+3+9+9=25>>25m. ### Answer: 25
Expected answer: 24
Correct? No
Problem: A rectangle has a length of 31m and a width of 6m. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of all of its sides. The perimeter of this rectangle is 31+6+31+6 = <<31+6+31+6=74>>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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of all of its sides. The perimeter of this rectangle is 43+6+43+6 = <<43+6+43+6=96>>96m. ### Answer: 96
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?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of this rectangle is 12 x 33 = <<12*33=396>>396 m^2. ### 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?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of this rectangle is 18 x 33 = <<18*33=594>>594 m^2. ### 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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The rectangle has 4 sides. The length of each side is 20m. The perimeter of the rectangle is 20+20+20+20 = <<20+20+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?
LLemma 7B:
The perimeter of a rectangle is the sum of the lengths of its sides. The length of the rectangle is 35m. The width of the rectangle is 9m. The perimeter of the rectangle is 35+9+35+9 = <<35+9+35+9=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?
LLemma 7B:
The perimeter of a rectangle is the sum of the lengths of its sides. The length of the rectangle is 26m. The width of the rectangle is 9m. The perimeter of the rectangle is 26+9+26+9 = <<26+9+26+9=69>>69m. ### Answer: 69
Expected answer: 70
Correct? No
Problem: A rectangle has a length of 9m and a width of 25m. What is the area of the rectangle?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of the rectangle is 9*25 = <<9*25=225>>225 m^2. ### 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?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of the rectangle is 16*9 = <<16*9=144>>144 m^2. ### 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?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of the rectangle is 13*43 = <<13*43=569>>569 m^2. ### Answer: 569
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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its width and its length. The perimeter of the rectangle is 27+47 = <<27+47=74>>74m. ### Answer: 74
Expected answer: 148
Correct? No
Problem: A rectangular football field has an area of 21m * 42m, calculate the area of the football field.
LLemma 7B:
Reasoning: The area of a rectangle is the product of its length and width. The area of the football field is 21m * 42m = <<21*42=862>>862m^2 ### Answer: 862
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?
LLemma 7B:
Reasoning: The area of the rectangle is 27*25 = <<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?
LLemma 7B:
Reasoning: The area of the rectangle is 11*25 = <<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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 45+48+45+48 = <<45+48+45+48=196>>196m. ### Answer: 196
Expected answer: 186
Correct? No
Problem: A rectangle has a length of 11 meters and a width of 7 meters. What is the perimeter of the rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 11+7+11+7 = <<11+7+11+7=36>>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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 10+7+10+7 = <<10+7+10+7=34>>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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The length of the field is 30m and the width is 2m. The perimeter of the field is 30+2+30+2 = <<30+2+30+2=64>>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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The length of the field is 20m and the width is 2m. The perimeter of the field is 20+2+20+2 = <<20+2+20+2=44>>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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all of its sides. The length of the rectangle is 7m. The width of the rectangle is 8m. The perimeter of the rectangle is 7+8 = <<7+8=15>>15m. ### Answer: 15
Expected answer: 30
Correct? No
Problem: A rectangle has a length of 14m and a width of 18m. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The length of the rectangle is 14m. The width of the rectangle is 18m. The perimeter of the rectangle is 14+18 = <<14+18=32>>32m. ### Answer: 32
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.
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 43+3+43+3 = <<43+3+43+3=99>>99 units. ### Answer: 99
Expected answer: 92
Correct? No
Problem: A rectangle has one side that measures 36 meters and another side that measures 42 meters. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The length of the rectangle is 36 meters. The width of the rectangle is 42 meters. The perimeter of the rectangle is 36+42 = <<36+42=78>>78 meters. ### Answer: 78
Expected answer: 156
Correct? No
Problem: A rectangle has a length of 1m and a width of 6m. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The length of the rectangle is 1m. The width of the rectangle is 6m. The perimeter of the rectangle is 1+6+1+6 = <<1+6+1+6=14>>14m. ### Answer: 14
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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The length of the rectangle is 28m. The width of the rectangle is 6m. The perimeter of the rectangle is 28+6+28+6 = <<28+6+28+6=58>>58m. ### Answer: 58
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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The perimeter of the rectangle is 45+45+8+8 = <<45+45+8+8=132>>132m. ### Answer: 132
Expected answer: 106
Correct? No
Problem: A rectangular garden has a length of 25 meters and a width of 37 meters. What is the perimeter of the garden?
LLemma 7B:
The perimeter of a rectangle is the sum of its length and width. The perimeter of the garden is 25+37 = <<25+37=62>>62 meters. ### Answer: 62
Expected answer: 124
Correct? No
Problem: A rectangle has length 36m and width 3m. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The length of the rectangle is 36m. The width of the rectangle is 3m. The perimeter of the rectangle is 36m + 3m = <<36+3=39>>39m. ### Answer: 39
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.
LLemma 7B:
The perimeter of a rectangle is the sum of its sides. The length of the garden is 45 meters. The width of the garden is 50 meters. The perimeter of the garden is 45+50 = <<45+50=95>>95 meters. ### Answer: 95
Expected answer: 190
Correct? No
Problem: A rectangle has a length of 44m and a width of 34m. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The length of the rectangle is 44m. The width of the rectangle is 34m. The perimeter of the rectangle is 44+34 = <<44+34=78>>78m. ### Answer: 78
Expected answer: 156
Correct? No
Problem: A rectangle has a length of 42 m and a width of 29 m. Calculate the perimeter of the rectangle.
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The length of the rectangle is 42 m. The width of the rectangle is 29 m. The perimeter of the rectangle is 42+29 = <<42+29=71>>71 m. ### Answer: 71
Expected answer: 142
Correct? No
Problem: A rectangle has a length of 44 meters and a width of 35 meters. What is the perimeter of the rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The length of the rectangle is 44 meters. The width of the rectangle is 35 meters. The perimeter of the rectangle is 44+35 = <<44+35=79>>79 meters. ### Answer: 79
Expected answer: 158
Correct? No
Problem: A rectangle has a length of 44m and a width of 45m. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of all of its sides. The perimeter of this rectangle is 44+45+44+45 = <<44+45+44+45=178>>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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of all of its sides. The perimeter of this rectangle is 44+48+44+48 = <<44+48+44+48=176>>176m. ### Answer: 176
Expected answer: 184
Correct? No
Problem: A rectangle has a length of 3 meters and a width of 39 meters. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its length and width. The perimeter of the rectangle is 3+39 = <<3+39=42>>42 meters. ### Answer: 42
Expected answer: 84
Correct? No
Problem: A rectangular garden has sides that measure 32m and 12m. What is the perimeter of this garden?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The perimeter of the garden is 32+12 = <<32+12=44>>44m. ### Answer: 44
Expected answer: 88
Correct? No
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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The length of the swimming pool is 24 feet. The width of the swimming pool is 6 feet. The perimeter of the swimming pool is 24+6 = <<24+6=30>>30 feet. ### Answer: 30
Expected answer: 60
Correct? No
Problem: A rectangle has a length of 27m and a width of 21m. What is the area of this rectangle?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of this rectangle is 27m x 21m = <<27*21=567>>567 m^2. ### Answer: 567
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?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of this rectangle is 27m x 8m = <<27*8=216>>216 m^2. ### Answer: 216
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?
LLemma 7B:
Reasoning: The length of the rectangle is 2*49=<<2*49=98>>98m. ### Answer: 98
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?
LLemma 7B:
Reasoning: The length of the rectangle is 2*18=<<2*18=36>>36m. ### Answer: 36
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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 2(50+36) = <<2(50+36)>>140m. ### Answer: 140
Expected answer: 172
Correct? No
Problem: A rectangle has a length of 8m and a width of 44m. What is the perimeter of the rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The length of the rectangle is 8m. The width of the rectangle is 44m. The perimeter of the rectangle is 8+44 = <<8+44=52>>52m. ### Answer: 52
Expected answer: 104
Correct? No
Problem: If a rectangle has a length of 47 feet and a width of 21 feet, what is the area of the rectangle?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of the rectangle is 47 x 21 = <<47*21=987>>987 square feet. ### Answer: 987
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?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of the rectangle is 21 x 15 = <<21*15=315>>315 square feet. ### Answer: 315
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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The length of the rectangle is 19m. The breadth of the rectangle is 28m. The perimeter of the rectangle is 19+28 = <<19+28=47>>47m. ### Answer: 47
Expected answer: 94
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?
LLemma 7B:
Reasoning: The area of a rectangle is the product of the length and width. The length of the rectangle is 39 meters. The width of the rectangle is 10 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?
LLemma 7B:
Reasoning: The area of a rectangle is the product of the length and width. The length of the rectangle is 37 meters. The width of the rectangle is 10 meters. The area of the rectangle is 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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle 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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 19+6+19+6 = <<19+6+19+6=48>>48 meters. ### Answer: 48
Expected answer: 50
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?
LLemma 7B:
Reasoning: The area of a rectangle is given by the equation length * width. If the length is 9m and the width is 26m, the area of the rectangle is 9*26 = <<9*26=234>>234m^2. ### 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?
LLemma 7B:
Reasoning: The area of a rectangle is given by the equation length * width. If the length is 47m and the width is 9m, the area of the rectangle is 47*9 = <<47*9=423>>423m^2. ### 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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The perimeter of the rectangle is 19+7+19+7 = <<19+7+19+7=53>>53cm. ### Answer: 53
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?
LLemma 7B:
Reasoning: The area of a rectangle is length times width. The area of the shutter is 10m x 6m = <<10*6=60>>60m^2. ### 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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 24+15+24+15 = <<24+15+24+15=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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 24+10+24+10 = <<24+10+24+10=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?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of the plot is 32 x 27 = <<32*27=864>>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?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of the plot is 32 x 18 = <<32*18=576>>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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all of its sides. The length of the rectangle is 15m. The width of the rectangle is 10m. The perimeter of the rectangle is 15+10 = <<15+10=25>>25m. ### Answer: 25
Expected answer: 50
Correct? No
Problem: A rectangle has a length of 44m and a width of 37m. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of all of its sides. The perimeter of this rectangle is 44+37+44+37 = <<44+37+44+37=158>>158m. ### Answer: 158
Expected answer: 162
Correct? No
Problem: A rectangle has length of 14 cm and width 8 cm. What is the perimeter of the rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 14+8+14+8 = <<14+8+14+8=44>>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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 14+18+14+18 = <<14+18+14+18=66>>66 cm. ### Answer: 66
Expected answer: 64
Correct? No
Problem: A rectangle has a length of 26m and a width of 28m. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of all of its sides. The perimeter of this rectangle is 26+28+26+28 = <<26+28+26+28=120>>120m. ### Answer: 120
Expected answer: 108
Correct? No
Problem: A rectangle has a length of 15m and a width of 37m. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 15+37+15+37 = <<15+37+15+37=109>>109m. ### Answer: 109
Expected answer: 104
Correct? No
Problem: A rectangle has a length of 42m and a width of 40m. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of all of its sides. The perimeter of this rectangle 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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of all of its sides. The perimeter of this rectangle is 42+24+42+24 = <<42+24+42+20=140>>140m. ### Answer: 140
Expected answer: 132
Correct? No
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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The perimeter of the garden is 21+30 = <<21+30=51>>51 feet. ### Answer: 51
Expected answer: 102
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?
LLemma 7B:
Reasoning: The area of a rectangle is the product of its length and width. The area of the playground is given as the product of 17 and 44. 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?
LLemma 7B:
Reasoning: The area of a rectangle is the product of its length and width. The length of the playground is 37 meters. The area of the playground is 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?
LLemma 7B:
The perimeter of a rectangle is the sum of its width and its length. The perimeter of rectangle ABCD is 47+50 = <<47+50=97>>97m. ### Answer: 97
Expected answer: 194
Correct? No
Problem: A rectangle has a length of 11m and a width of 31m. What is the perimeter of the rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 11+31+11+31 = <<11+31+11+31=83>>83m. ### Answer: 83
Expected answer: 84
Correct? No
Problem: A rectangular garden has a length of 39m and a width of 19m. What is the area of this garden?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of the garden is 39 x 19 = <<39*19=741>>741 m^2. ### 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?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of the garden is 35 x 19 = <<35*19=665>>665 m^2. ### 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?
LLemma 7B:
Reasoning: The area of a rectangle is the product of its length and width. The 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. The area of the wooden plank is 29 x 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?
LLemma 7B:
Reasoning: The area of a rectangle is the product of its length and width. The carpenter decided to cut the same 29 cm wide wooden plank into shorter lengths of 5 cm each. The area of one of these shorter cut wooden planks is 29 x 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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 25+11+25+11 = <<25+11+25+11=71>>71m. ### Answer: 71
Expected answer: 72
Correct? No
Problem: A rectangle has a length of 49m and a breadth of 9m. What is the perimeter of the rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is 2(l+b) = 2(49+9) = 2(58) = <<2*58=116>>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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is 2(l+b) = 2(49+19) = 2(68) = <<2*68=136>>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?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of this rectangle is 16 x 7 = <<16*7=112>>112 m^2. ### 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?
LLemma 7B:
Reasoning: The perimeter of the playground is 2*(14+2) = <<2*(14+2)>>30m. ### Answer: 30
Expected answer: 32
Correct? No
Problem: A square has a side length of 16 units. What is the perimeter of the square?
LLemma 7B:
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?
LLemma 7B:
The perimeter of a rectangle is the sum of the lengths of its sides. The perimeter of the rectangle is 22+16+22+16 = <<22+16+22+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?
LLemma 7B:
The perimeter of a rectangle is the sum of its width and its length. The perimeter of this garden is 7+21 = <<7+21=28>>28 meters. ### Answer: 28
Expected answer: 56
Correct? No
Problem: A rectangle has a length of 20 meters and a width of 5 meters. What is the area of the rectangle?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of the rectangle is 20 x 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?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of the rectangle is 20 x 17 = <<20*17=340>>340 square meters. ### Answer: 340
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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 37+43+37+43 = <<37+43+37+43=171>>171m. ### Answer: 171
Expected answer: 160
Correct? No
Problem: A rectangle has a length of 9m. If the width of the rectangle is 1m, what is the area?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of the rectangle is 9*1 = <<9*1=9>>9 m^2. ### Answer: 9
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?
LLemma 7B:
Reasoning: The area of a rectangle is the length times the width. The area of the rectangle is 9*40 = <<9*40=360>>360 m^2. ### Answer: 360
Expected answer: 360
Correct? Yes
Problem: A rectangle's area is the product of 22m and 23m. What is the area of the rectangle?
LLemma 7B:
Reasoning: The area of a rectangle is the product of its length and width. The area of the rectangle is 22m x 23m = <<22*23=486>>486 square meters. ### Answer: 486
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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all of its sides. The length of the rectangle is 14 cm. The width of the rectangle is 21 cm. The perimeter of the rectangle is 14+21 = <<14+21=35>>35 cm. ### Answer: 35
Expected answer: 70
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?
LLemma 7B:
Reasoning: The area of a rectangle is the product of its length and width. The area of the swimming pool is 23*12 = <<23*12=276>>276 square meters. ### Answer: 276
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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 39+8+39+8 = <<39+8+39+8=94>>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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The perimeter of the rectangle is 39+23+39+23 = <<39+23+39+23=115>>115 meters. ### Answer: 115
Expected answer: 124
Correct? No
Problem: A rectangle has a width of 27m and a length of 40m. What is the perimeter of the rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its width and its length. The perimeter of the rectangle is 27+40 = <<27+40=67>>67m. ### Answer: 67
Expected answer: 134
Correct? No
Problem: A rectangle's length is 35m and its width is 9m. What is the perimeter of the rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of its sides. The rectangle's perimeter is 35+9+35+9 = <<35+9+35+9=98>>98m. ### Answer: 98
Expected answer: 88
Correct? No
Problem: A rectangle has a length of 38m and a width of 11m. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of all of its sides. The perimeter of this rectangle is 38+11+38+11 = <<38+11+38+11=96>>96m. ### Answer: 96
Expected answer: 98
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?
LLemma 7B:
Reasoning: The area of a rectangle is the product of its two sides. The area of this rectangle is 28 x 29 = <<28*29=812>>812 m^2. ### Answer: 812
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?
LLemma 7B:
Reasoning: The area of a rectangle is the product of its two sides. The area of this rectangle is 28 x 35 = <<28*35=980>>980 m^2. ### Answer: 980
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?
LLemma 7B:
Reasoning: The perimeter of a square is 4 times the side length. The perimeter of the square is 4*9 = <<4*9=36>>36m. ### 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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of all of its sides. The perimeter of this rectangle is 38+29+38+29 = <<38+29+38+29=134>>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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of all of its sides. The perimeter of this rectangle is 6+29+6+29 = <<6+29+6+29=84>>84m. ### Answer: 84
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.
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of its sides. The length of the rectangle is 45m. The width of the rectangle is 47m. The perimeter of the rectangle is 45+47 = <<45+47=92>>92m. ### Answer: 92
Expected answer: 184
Correct? No
Problem: Given a rectangle where the length is 24m and the width is 20m, what is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is the sum of the lengths of all the sides. The length of the rectangle is 24m. The width of the rectangle is 20m. The perimeter of the rectangle is 24+20 = <<24+20=44>>44m. ### Answer: 44
Expected answer: 88
Correct? No
Problem: The length and width of a rectangle are both 32m. What is the perimeter of this rectangle?
LLemma 7B:
Reasoning: The perimeter of a rectangle is 2(length + width). The perimeter of this rectangle is 2(32+32) = <<2(32+32)=128>>128m. ### Answer: 128
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?
LLemma 7B:
Reasoning: The perimeter of a rectangle is 2(length + width). The perimeter of this rectangle is 2(32+13) = <<2(32+13)=100>>100m. ### Answer: 100
Expected answer: 90
Correct? No