SOLUTION: The area of a triangle is 96 sq. inches. Its altitude is 2 inches greater than five times its base. Find the altitude. ( A= 1/2bh ) I tried 96=1/2(5b)h help please.

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Question 190818: The area of a triangle is 96 sq. inches. Its altitude is 2 inches greater than five times its base. Find the altitude. ( A= 1/2bh )
I tried 96=1/2(5b)h
help please.
Found 2 solutions by edjones, nerdybill:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
a=5b+2
ab/2=A
(5b+2)b/2=96
(5b+2)b=192
5b^2+2b=192
5b^2+2b-192=0
b=6 Quadratic formula (below)
a=32
.
Ed
.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B2x%2B-192+=+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=%282%29%5E2-4%2A5%2A-192=3844.

Discriminant d=3844 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+3844+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+3844+%29%29%2F2%5C5+=+6
x%5B2%5D+=+%28-%282%29-sqrt%28+3844+%29%29%2F2%5C5+=+-6.4

Quadratic expression 5x%5E2%2B2x%2B-192 can be factored:
5x%5E2%2B2x%2B-192+=+%28x-6%29%2A%28x--6.4%29
Again, the answer is: 6, -6.4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B2%2Ax%2B-192+%29

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a triangle is 96 sq. inches. Its altitude is 2 inches greater than five times its base. Find the altitude. ( A= 1/2bh )
.
Let b = base
then
5b-2 = altitude or height
.
therefore applying:
A= 1/2bh
we have
96 = (1/2)b(5b-2)
96 = (1/2)b(5b-2)
192 = b(5b-2)
192 = 5b^2 - 2b
0 = 5b^2 - 2b - 192
Apply the quadratic equation to solve for b (details below):
b = {6.464, -6.064}
We can toss out the negative solution so we get:
b = 6.464 inches (base)
.
To find the height or altitude:
5b-2 = 5(6.464)-2 = 30.32 inches (altitude)
.
Details of quadratic equation below:
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ab%5E2%2Bbb%2Bc=0 (in our case 5b%5E2%2B-2b%2B-196+=+0) has the following solutons:

b%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=%28-2%29%5E2-4%2A5%2A-196=3924.

Discriminant d=3924 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+3924+%29%29%2F2%5Ca.

b%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+3924+%29%29%2F2%5C5+=+6.46418390534633
b%5B2%5D+=+%28-%28-2%29-sqrt%28+3924+%29%29%2F2%5C5+=+-6.06418390534633

Quadratic expression 5b%5E2%2B-2b%2B-196 can be factored:
5b%5E2%2B-2b%2B-196+=+5%28b-6.46418390534633%29%2A%28b--6.06418390534633%29
Again, the answer is: 6.46418390534633, -6.06418390534633. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-2%2Ax%2B-196+%29