Question

The length of a rectangle is 4 inches more than its width. The area of the rectangle is equal to 4 inches less than 5 times the perimeter. Find the length and width of the rectangle.

Answer 1

P = 2(L + W)
L = W + 4
A = 5P - 4

P = 2(W + 4 + W)
P = 2(2W + 4)
P = 4W + 8

A = 5(4W + 8) - 4
A = 20W + 36

A = L * W
A = W(W + 4)
A = W^2 + 4W

W^2 + 4W = 20W + 36
W^2 - 20W + 4W - 36 = 0
W^2 - 16W - 36 = 0
(W + 2)(W - 18) = 0

W - 18 = 0
W = 18

L = W + 4
L = 18 + 4
L = 22

A = L * W
A = 18 * 22
A = 396

P = 4W + 8
P = 4(18) + 8
P = 72 + 8
P = 80

length = 22, width = 18, area = 396, perimeter = 80