SOLUTION: The perimeter of a rectangle is 30 inches, and its area is 54 square inches. Find the length of the longest side of the rectangle.

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Question 1004071: The perimeter of a rectangle is 30 inches, and its area is 54 square inches. Find the length of the longest side of the rectangle.
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
From the facts we have
P = 2L + 2W = 30 and
A = LW = 54
Solve the first for W and substitute into the second one...
2L + 2W = 30
L + W = 15
W = 15 - L
and then
L(15 - L) = 54
-L^2 + 15L - 54 = 0
or
L^2 - 15L + 54 = 0
Factoring we get
(L - 9)(L - 6) = 0
L = 9 in
W = 6 in