Question 285409: find the dimensions of a retangle if its perimeter is 50 feet and its area is 150 square feet?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! P = perimeter = 2L + 2W = 2(L+W)
P = 50
so...
L+W = 25
.
A = area = L*W
A = 150
.
That means we know:
L + W = 25
and
L*W =150
.
Substituting L = 25-W,
.
(25-W)*W = 150
25W -W^2 = 150
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Add W^2 to both sides
.
25W = W^2 + 150
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Subtract 25W from both sides
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0 = W^2 - 25W + 150
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Factoring
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(W-10)(W-15) = 0
.
That means W can be either 10 or 15.
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Since L = 25-W, L can be either 15 or 10, depending on W.
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Checking our work
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Is P = 50 if W=15?
2L + 2W = 2(10)+2(15) = 20+30= 50
Is P = 50 if L=15?
2L + 2W = 2(15)+2(10) = 50
.
Either way the area is 150 because we know 10*15 = 15*10 = 150.
.
Answer:
L = 10 and W = 15
OR
L = 15 and W = 10
.
Done
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