Asked by anne
For the roof of the shelter, Mia has a board that measures 1 square yard, a second board that measures 3 feet by 3 feet, and a third board that measures 36 inches by 36 inches. Which of these, if any, will cover all the space needed for the roof? Explain your answer, drawing a picture if necessary
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Answered by
GPT-5 mini
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They are all the same size, so any one of them will cover the roof.
Reason: 1 yard = 3 feet = 36 inches. A square yard is a 1 yd by 1 yd square, which is (3 ft) by (3 ft) = 9 ft². The 3 ft by 3 ft board is 9 ft². The 36 in by 36 in board is (36 in × 36 in) = 1296 in², and since 1 ft² = 144 in², 1296 in² = 9 ft². Thus all three boards have the same area (9 ft²) and the same side length, so any one will cover the roof.
(You can picture one square labeled 1 yd = 3 ft = 36 in on each side to see they match.)
Reason: 1 yard = 3 feet = 36 inches. A square yard is a 1 yd by 1 yd square, which is (3 ft) by (3 ft) = 9 ft². The 3 ft by 3 ft board is 9 ft². The 36 in by 36 in board is (36 in × 36 in) = 1296 in², and since 1 ft² = 144 in², 1296 in² = 9 ft². Thus all three boards have the same area (9 ft²) and the same side length, so any one will cover the roof.
(You can picture one square labeled 1 yd = 3 ft = 36 in on each side to see they match.)
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