SOLUTION: A rectangle has a perimeter of 50 cm. Is it possible to have an area of 136 cm^2? If so, what are the dimensions?

Question 290178: A rectangle has a perimeter of 50 cm. Is it possible to have an area of 136 cm^2? If so, what are the dimensions?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A rectangle has a perimeter of 50 cm.
Is it possible to have an area of 136 cm^2? If so, what are the dimensions?
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Equations:
2(L+W) = 50
LW = 136
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Modify:
L = 25-W
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Substitute:
(25-W)W = 136
25W - W^2 = 136
W^2 - 25W +136 = 0
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Check the discrimant to see if there is a solution:
(25)^2 -4*1*136 is greater than zero so there is a solution.
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What are the dimensions?
w = [25 +- sqrt(25^2-4*136)]/2
W = [25 +- sqrt(81)]/2
W = [25 +- 9]/2
w = (34/2) or W = 16/2
W = 17 or W = 8
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If W = 17, L = 8
If W = 8, L = 17
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Cheers,
Stan H.
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