Question

Explain why it's possible to draw more than two different rectangles with an area of 36 square units but if not possible draw more than two different rectangles with an area of 15 square units the side of the rectangles are whole numbers

Answer 1

The area of a rectangle is the result of multiplying its length times its width. So the rectangles length and width are factor pairs of the area.

The number 36 has four non-equal, whole number factor pairs: (1,36) ; (2,18) ; (3,13) ; (4,9)

*note : (6,6) makes a square not rectangle

The number 15 has only two whole number factor pairs (1,15) and (3,5)