A rectangle is twice as long as it is wide. If its length is increased by 4 inches and its width is increased by 2 inches, its area is increased by 64 in^2. Find its original dimensions. 1

Answer 1

L=2W, (L+4)(W+2) = LW + 64

(2W+4)(W+2) = (2W)W + 64

2W^2 + 8W + 8 = 2W^2 + 64

8W = 64- 8 = 56

W = 56/8 = 7 inches width

L=2W = 14 inches width

original area was LW = 98 square inches

new area = 18(9) = 162 = 98+64