SOLUTION: The perimeter of a rectangle is 34 inches, and its area is 60 square inches. What is the product of the lengths of the diagonals, in square inches?

Algebra ->  Rectangles -> SOLUTION: The perimeter of a rectangle is 34 inches, and its area is 60 square inches. What is the product of the lengths of the diagonals, in square inches?       Log On


   

Question 973020: The perimeter of a rectangle is 34 inches, and its area is 60 square inches. What is the product of the lengths of the diagonals, in square inches?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The perimeter of a rectangle is 34 inches,
2L + 2W = 34
simplify, divide by 2
L + W = 17
L = (17-W)
and its area is 60 square inches.
L*W = 60
Find the dimensions, replace L with (17-W) in the area equation
W(17-W) = 60
-W^2 + 17W - 60 = 0
Multiply equation by -1
W^2 - 17W + 60 = 0
Factors to
(W-5)(W-12) = 0
W = 5, then L=12
W = 12, then L=5
:
What is the product of the lengths of the diagonals, in square inches?
%28sqrt%2812%5E2%2B5%5E2%29%29%5E2 = 144 + 25 = 169 sq inches