SOLUTION: I need help with this problem. The perimeter of a rectangle is 44 inches, and its area is 112 square inches. Find the length and width of the rectangle.

Algebra ->  Rectangles -> SOLUTION: I need help with this problem. The perimeter of a rectangle is 44 inches, and its area is 112 square inches. Find the length and width of the rectangle.       Log On


   

Question 209856: I need help with this problem. The perimeter of a rectangle is 44 inches, and its area is 112 square inches. Find the length and width of the rectangle.
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
2L+2W=44
LW=112
L=112/W
2(112/W)+2W=44
(224/W)+2W=44
(224+2W*W)/W=44
224+2W^2=44*W
224+2W^2=44W
2W^2-44W+224=0
2(W^2-22W+112)=0
2(W-14)(W-8)=0
W-14=0
W=14 ANS. L=112/14=8 ANS.
W-8=0
W=8 ANS. L=112/8=14 ANS.
PROOF:
8*14=112
2*14+2*8=44
28+16=44
44=44