SOLUTION: Please help me with this problem:The floor of a cabin is shaped like a rectangle. It has a surface area of 288 square feet. If the perimeter of the floor is 68 feet, what is the le

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Question 956109: Please help me with this problem:The floor of a cabin is shaped like a rectangle. It has a surface area of 288 square feet. If the perimeter of the floor is 68 feet, what is the length of the floor?
Found 2 solutions by Alan3354, macston:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me with this problem:The floor of a cabin is shaped like a rectangle. It has a surface area of 288 square feet. If the perimeter of the floor is 68 feet, what is the length of the floor?
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P = 2L + 2W = 68
L + W = 34
L*W = 288
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Find a pair of factors of 288 with a sum of 34.
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1*288 NG
2*144 NG
3*96 NG
etc

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
L=length;W=width; P=perimeter=68ft; A=area=288 sq ft
A=L*W
L=A/W
P=2(L+W) Substitute for L
68ft=2((A/W)+W) Divide each side by 2
34ft=(288sqft/W)+W Subtract W from each side.
34ft-W=288sqft/W Multiply each side by W
-W%5E2%2B34W=288 Subtract 288 from each side.
-W%5E2%2B34W-288=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case -1W%5E2%2B34W%2B-288+=+0) has the following solutons:

W%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2834%29%5E2-4%2A-1%2A-288=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-34%2B-sqrt%28+4+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%2834%29%2Bsqrt%28+4+%29%29%2F2%5C-1+=+16
W%5B2%5D+=+%28-%2834%29-sqrt%28+4+%29%29%2F2%5C-1+=+18

Quadratic expression -1W%5E2%2B34W%2B-288 can be factored:
-1W%5E2%2B34W%2B-288+=+-1%28W-16%29%2A%28W-18%29
Again, the answer is: 16, 18. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B34%2Ax%2B-288+%29

The width is 16ft or 18ft and length is the other.
ANSWER: The dimensions are 18 feet by 16 feet.
CHECK:
P=2(L+W)
68ft=2(18ft+16ft)
68ft=2(34ft)
68ft=68ft
A=LW
288 sq ft=(18ft)(16ft)
288 sq ft=288 sq ft