A rectangle is 8cm longer than it is wide. IF its length and width are both decreased by 2cm, its area is decreased by 108cm^2 . Find its original dimensions

Question

Area Problems

Answer 1

Let x represent width of the original rectangle.

Then x + 8 represents the length of the original rectangle.

The area of the original is represented as x (x+8).

For the new rectangle the width is (x- 2) and its length is (x+6).

The area of the new rectangle is ( x - 2) (x + 6).

Area of new IS 108 less than area of original.

(x - 2) (x + 6) = x(x+8) - 108

x² + 4x -12 = x² + 8x -108 [x² terms cancel]

-4x = -96

x = 24

x + 8 = 32

Area of original = 768

Area of new:

22(30) = 660

768 - 660 = 108 (check)