Question

A rectangle is drawn so the width is 14 inches longer than the height .If the rectangle’s diagonal measurement is 34 inches, find the height

Answer 1

Let the height be represented as x

width = 14 + x

Length of diagonal = 34 inches.

Taking one diagonal of the rectangle to form a triangle.

using the Pythagoras theorem.

34² = (14 + x)² + x²

1156 = 196 + 28x + x² + x²

2x² + 28x - 960 = 0

divide through by 2

x² + 14x - 480 = 0

x² + 30x - 16x - 480 = 0

x(x + 30) - 16 (x + 30) = 0

(x - 16) = 0 or (x + 30) = 0

x = 16 or x = - 30

since the length can't be negative

therefore 16 inches is correct