The length of a rectangle is 10 feet longer than it is wide. If each side is increased 10 feet, then the area is multiplied by 4. What was the size of the original rectangle?

Question

The length of a rectangle is 10 feet longer than it is wide. If each side is increased 10 feet, then the area is multiplied by 4. What was the size of the original rectangle?

Answer 1

Draw and label a diagram

A_original = (w)(w + 10)

A_enlarged = (w + 10)(w + 20)

A_enlarged = 4 A_origianl

(w + 10)(w + 20) = 4(w)(w + 10)

w² + 30w + 200 = 4w² + 40w

0 = 3w² + 10w - 200

0 = (w + 10)(3w - 20)

w = 20 / 3

What is the length? What is the area?