Suppose you want to build a rectangular sandbox where the width is 5 feet less than the length and the diagonal is 5 feet longer than the length. what are the dimensions of the sandbox?

Let L = length

W = L - 5 ←5 feet less than (reverse order - ) the length (L)

D = L + 5

These 3 lengths form a right triangle with D being the hypotenuse, c.

Using the Pythagorean Theorem, a² + b² = c²

L² + (L - 5) ² = (L + 5) ²

L² + L² - 10L + 25 = L² + 10L + 25

L² - 20L = 0

L = 0 (can't use this answer) or L = 20 (this is a usable answer)

Dimensions of the sandbox 20 ft by 15 ft

Length = 20 ft

Width = 15 ft

Diagonal = 25 ft