The lengths of two opposing sides of a square are decreased by forty percent. By approximately what percent would the lengths of the other two sides have to be INCREASED so that the area of the new figure ( a rectangle) is the same as the area of the original square?

Question

The lengths of two opposing sides of a square are decreased by forty percent. By approximately what percent would the lengths of the other two sides have to be INCREASED so that the area of the new figure ( a rectangle) is the same as the area of the original square?

Answer 1

Let a = the original square side length.

Reducing it by 40% leaves two opposing sides of the rectangle with length 0.6a. Let the other two sides' length be x

0.6a * x = a^2

x = a/0.6 = 5/3 * a

The other two side lengths must be inceased by 66.7% to keep the area the same.