The length of a rectangular area rug in a room is 5 feet longer than the width, w. The owner wants to get a new rug that is 2 feet longer on each side. What is the equation of the area of the new rug

Answer 1

L=5+W

original area = LW = (5+W)W = 5W + W^2

2 feet longer on each side means new length = L+2 and new width = W+2

new area

A(W) = (2+5+W)(2+W)

= (7+W)(2+W)

= 14 + 9W + W^2

or in terms of L

New Area

A(L) = (7+L-5)(2+L-5)

= (L+2)(L-5)

= L^2 -3L -15