SOLUTION: the width of a rectangle is 8 feet less than the length. The area is 128square feet. what is the length and width

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Question 690565: the width of a rectangle is 8 feet less than the length. The area is 128square feet. what is the length and width
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Set-Up
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A = L * W (Area of a rectangle)
Given: A = 128, L = W + 8
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Solution:
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Substitute the given information into the equation for the area of a rectangle
%28128%29+=+%28W+%2B+8%29+%2A+W Simplify
128+=+W%5E2+%2B+8W Subtract 128 from both sides
0+=+W%5E2+%2B+8W+-+128
Use the quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case 1W%5E2%2B8W%2B-128+=+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=%288%29%5E2-4%2A1%2A-128=576.

Discriminant d=576 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+576+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%288%29%2Bsqrt%28+576+%29%29%2F2%5C1+=+8
W%5B2%5D+=+%28-%288%29-sqrt%28+576+%29%29%2F2%5C1+=+-16

Quadratic expression 1W%5E2%2B8W%2B-128 can be factored:
1W%5E2%2B8W%2B-128+=+1%28W-8%29%2A%28W--16%29
Again, the answer is: 8, -16. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B-128+%29


The answers were W = 8feet or -16feet. but since you can not have a negative width. Just use the 8
Now we can find the length
L =W + 8
Plug 8 in for W
L+=+8+%2B%288%29
highlight_green%28L+=+16+feet%29