A school playground is a 25 m by 40 m rectangle.

Question

A school playground is a 25 m by 40 m rectangle. The school increases the width to 40 m and increases the length so that the original rectangle and the new one are similar. By how much does the perimeter of the playground increase?

Answer 1

To be similar the length must be increased by the same ratio as the width. The new width is 40/25, or 8/5, of the original. Therefore the new length must be 8/5 of the original. The new length is (8/5)(40), or 64.

 

The change in area is equal to the square of the ratio of change. The new area is 64/25 or the original.