SOLUTION: the area of a parallelogramis 10in. the height is 2in. more than half the base. what is the base?...... how do you find this out?!

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Question 184318: the area of a parallelogramis 10in. the height is 2in. more than half the base. what is the base?...... how do you find this out?!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
the area of a parallelogramis 10in. the height is 2in. more than half the base. what is the base?...... how do you find this out?!
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Area = base times height
Here's what is given:
A = bh = 10 (Square inches, not inches)
h = (b/2) + 2 the height is 2in. more than half the base.
Substitute for h in the Area formula
A = b*(b/2 + 2) = 10
b%5E2%2F2+%2B+2b+=+10
b%5E2+%2B+4b+-+20+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-20+=+0) has the following solutons:

x%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=%284%29%5E2-4%2A1%2A-20=96.

Discriminant d=96 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+96+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+96+%29%29%2F2%5C1+=+2.89897948556636
x%5B2%5D+=+%28-%284%29-sqrt%28+96+%29%29%2F2%5C1+=+-6.89897948556636

Quadratic expression 1x%5E2%2B4x%2B-20 can be factored:
1x%5E2%2B4x%2B-20+=+%28x-2.89897948556636%29%2A%28x--6.89897948556636%29
Again, the answer is: 2.89897948556636, -6.89897948556636. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-20+%29

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Ignore the negative result.
b = -2 + 2sqrt(6)
b = ~2.899 inches