SOLUTION: The Perimeter of a rectangle is 26 cm and its area is 36 cm squared. What are the lengths of its two sides? How do I do this

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Question 721593: The Perimeter of a rectangle is 26 cm and its area is 36 cm squared. What are the lengths of its two sides? How do I do this
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
P = 2L + 2W = 26


A = L x W = 36


Solve the second equation for L in terms of W, and then plug that into the first equation. L=36/W


2(36/W) + 2W = 26 ---> multiply everything by W and multiply 36 by 2 -->72 + 2W^2 =26W


Subtract 26W from both sides.


2W^2 - 26W +72 = 0 (divide all terms by 2 to simplify) w^2 - 13W + 36 = 0


That factors to (W-9)(W-4)=0 so W = 9 or W = 4


W=9 works, but that would then be the longer side (L) so discard it for W.


A = L X 4 = 36 so L = 36/4 = 9.

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