SOLUTION: Their is a rectangle and its legnth is d-12 and the width is d. If the area is 28 square units, what is the value of d?

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Question 446629: Their is a rectangle and its legnth is d-12 and the width is d. If the area is 28 square units, what is the value of d?
Found 2 solutions by chriswen, stanbon:
Answer by chriswen(106) About Me  (Show Source):
You can put this solution on YOUR website!
A=l*w
28=(d)(d-12)
28=d^2-12d
d^2-12d-28=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ad%5E2%2Bbd%2Bc=0 (in our case 1d%5E2%2B-12d%2B-28+=+0) has the following solutons:

d%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=%28-12%29%5E2-4%2A1%2A-28=256.

Discriminant d=256 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--12%2B-sqrt%28+256+%29%29%2F2%5Ca.

d%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+256+%29%29%2F2%5C1+=+14
d%5B2%5D+=+%28-%28-12%29-sqrt%28+256+%29%29%2F2%5C1+=+-2

Quadratic expression 1d%5E2%2B-12d%2B-28 can be factored:
1d%5E2%2B-12d%2B-28+=+1%28d-14%29%2A%28d--2%29
Again, the answer is: 14, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-12%2Ax%2B-28+%29

The answer must be positive so the answer is 14.
d=14
d-12=2

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
There is a rectangle and its length is d-12 and the width is d. If the area is 28 square units, what is the value of d?
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Area = length*width
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28 = (d-12)d
d^2-12d-28 = 0
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Factor using Inverse FOIL:
d^2-14d+2d-28 = 0
d(d-14)+2(d-14) = 0
(d-14)(d+2) = 0
----
Positive solution:
width = d = 14
length = d-12 = 2
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Cheers,
Stan H.