SOLUTION: A dog trainer has 92 ft of fencing that will be used to create a rectangular work area for dogs. If the trainer wants to enclose an area of 408 ft2, what will be the dimensions of

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A dog trainer has 92 ft of fencing that will be used to create a rectangular work area for dogs. If the trainer wants to enclose an area of 408 ft2, what will be the dimensions of       Log On


   



Question 1056445: A dog trainer has 92 ft of fencing that will be used to create a rectangular work area for dogs. If the trainer wants to enclose an area of 408 ft2, what will be the dimensions of the work area?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
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A dog trainer has 92 ft of fencing that will be used to create a rectangular work area for dogs. If the trainer wants to enclose an area of 408 ft2, what will be the dimensions of the work area?
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P = 2W + 2L = 92
W + L = 46
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Area = W*L = 408
408 = 2*2*2*3*17
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Find a pair of factors of 408 with a sum of 46.
Hint: they're integers.

Answer by ikleyn(52805) About Me  (Show Source):
You can put this solution on YOUR website!
.
A dog trainer has 92 ft of fencing that will be used to create a rectangular work area for dogs.
If the trainer wants to enclose an area of 408 ft2, what will be the dimensions of the work area?
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L + W = 92%2F2  ====>  L + w = 46.

L = 46-W,

W*L = 408  --->  W*(46-W) = 408,

W^2 -46W + 408 = 0,

W%5B1%2C2%5D = %2846+%2B-+sqrt+%2846%5E2-4%2A408%29%29%2F2 = %2846+%2B-+sqrt%28484%29%29%2F2 = %2846+%2B-+22%29%2F2.

The only positive root is 34.

Answer. The dimensions are 34 ft and 46-34 = 12 ft.
        The length is 34 ft, the width is 12 ft.