SOLUTION: The perimiter of a rectangular concrete slab is 60 feet and its area is 224 square feet. What is the length of the longer side of the slab?

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Question 84735: The perimiter of a rectangular concrete slab is 60 feet and its area is 224 square feet. What is the length of the longer side of the slab?
Answer by PS(13) About Me  (Show Source):
You can put this solution on YOUR website!
length of the rectangular slab = L
width of the rectangular slab = W
Perimeter = 2L + 2W = 60
Area = L*W = 224
L = 224%2FW
Perimeter = 2%2A%28224%2FW%29+%2B+2W = 60
448+%2B+2%2AW%5E2 = 60%2AW
W%5E2+%2B+224 = 30%2AW
W%5E2+-+30%2AW+%2B+224 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case 1W%5E2%2B-30W%2B224+=+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=%28-30%29%5E2-4%2A1%2A224=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--30%2B-sqrt%28+4+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%28-30%29%2Bsqrt%28+4+%29%29%2F2%5C1+=+16
W%5B2%5D+=+%28-%28-30%29-sqrt%28+4+%29%29%2F2%5C1+=+14

Quadratic expression 1W%5E2%2B-30W%2B224 can be factored:
1W%5E2%2B-30W%2B224+=+1%28W-16%29%2A%28W-14%29
Again, the answer is: 16, 14. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-30%2Ax%2B224+%29


%28W-16%29+%2A+%28W-14%29 = 0
W = 16 or W = 14
The longer side is therefore 16