The length of a rectangle is 8ft more than the width.If the width is increased by 4 feet,and the length is decreased by 5 feet,the area remains the same.Find the dimensions of the original rectangle

Question

The length of a rectangle is 8 feet more than the width. If the width is increased by 4 feet, and the length is decreased by 5 feet, the area remains the same. Find the dimensions of the original rectangle.

Answer 1

The length of a rectangle is 8 feet more than the width. If the width is increased by 4 feet, and the length is decreased by 5 feet, the area remains the same. Find the dimensions of the original rectangle.

If L = length and W = width

First rectangle

L = w + 8

Second rectangle

W =W + 4 L = (w + 8) - 5 = w + 3

If the areas are the same, A1 = A 2 amd this gives us

(w + 8)w = (w + 4) (w + 3)

w² + 8w = w² + 7w +12 subtract w² from both sides

8w = 7w + 12 subtract 7w

w = 12

original rectangle is 20 x 12

Patti D.