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Explain why it is possible to draw more than two different rectangles with an area of 36 square units, but it is not possible to draw more than two different rectangles with an area of 15 square units. The sides of the rectangles are whole numbers.

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thisisbenmanley
It is possible to draw more than two different rectangles with an area of 36 square units because there is more than one pair of whole numbers that multiply to 36.  A 36 square unit rectangle could be made by 1x36, 2x18, 3,12, 4x9, or 6x6.

A 15 square unit triangle, however, can only be made with 1x15 and 3x5 because those are the only whole numbers that divide evenly into 15.
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