Length and width of a rectangle

Question

A rectangle is drawn so the width is 7 inches longer than the height. If the rectangle's diagonal measurement is 17 inches, find the height.

 

Give your answer rounded to 1 decimal place.

Answer 1

Use Pythagorean Theorem:

 

A² + B² =C²

 

x² + (x+7)² = 17²

 

x² + x² + 14x + 49 = 17^s

 

Combining and setting the equation equal to zero:

 

x²+7x-120 = 0

 

Factor:

 

(x-8)(x+15) = 0

 

x = 8 and x = -15.

 

Choose the positive solution since measure cannot be negative.

 

The height is 8 inches.