A rectangle is drawn so the width is 7 inches longer than the height. If the rectangle's diagonal measurement is 46 inches, find the height.

Answer 1

Use the Pythagorean theorem:

a^2 + b^2 = c^2

x = height
x + 7 = width

Therefore:

x^2 + (x + 7)^2 = 46^2

Expand and try to factor. If this does not factor easily, use the quadratic formula to solve.

Answer 2

A rectangle is drawn so the width is 3 inches longer than the height. If the rectangle's diagonal measurement is 55 inches, find the height.