SOLUTION: the perimeter of a rectangle is 40 inches and its area is 91 square inches find the length and width of the rectangle. solve step by step. There are 10 steps

Algebra ->  Rectangles -> SOLUTION: the perimeter of a rectangle is 40 inches and its area is 91 square inches find the length and width of the rectangle. solve step by step. There are 10 steps      Log On


   

Question 1077369: the perimeter of a rectangle is 40 inches and its area is 91 square inches find the length and width of the rectangle. solve step by step. There are 10 steps
Answer by math_helper(2461) About Me  (Show Source):
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2L + 2W = 40 (1) —> L+W=20
LW = 91 (2)
L = 91/W —> Substitute this into (1):
(91/W) + W = 20
91%2BW%5E2+=+20W+ <— multiplied both sides by W
+W%5E2-20W%2B91+=+0+
+%28W-13%29%28W-7%29+=+0+
W=7 or W=13
W=7 —> L=13
W=13 —> L=7 (let's reject this as L>W is the convention when describing rectangles)
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Ans: L=13in, W=7in
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Check: Area = LxW = 13in*7in = 91 sq in (ok)
Perimeter = 2L+2W=2(13in) + 2(7in) = 26in+14in = 40in (ok)
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