Explain why it is possible to draw 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 an area of 15 square units. the sides of the rectangles are whole numbers.

Area of rectangle = length × width

Given the area of rectangle = 36, we can list all the possible pairs of whole numbers that multiply to give

1 × 36 = 36
2 × 18 = 36
3 × 12 = 36
4 × 9 = 36
6 × 6 = 36 ⇒ This measurement will produce a square

Each pair of numbers represents the combination of length and width a rectangle might have in order to have an area of 36 units ² and we can have four different combinations.



Given area = 15

The pairs of whole numbers that multiply to give 15 are

1 × 15 = 15
3 × 5 = 15

There are only two pairs whole number that multiplies to give 15 and this is the reason why we can't have more than two combinations of length and width that would give us an area of 15 units²