Question

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

Answer 1

15 = 1*15 = 3*5
36= 1*36 = 2*18 = 3*12 = 4*9 = 6*6
Because only two whole number factor pairs make up 15, there are only two possible rectangles with whole number side lengths.
Because only five whole number factor pairs make up 36, there are only five possible rectangles with whole number side lengths.