SOLUTION: The height of a triangle is 10 inches less than the three times the base. the area is 156 square inches. what is the base of the triangle?

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Question 600854: The height of a triangle is 10 inches less than the three times the base. the area is 156 square inches. what is the base of the triangle?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
The height of a triangle is 10 inches less than the three times the base. the area is 156 square inches. what is the base of the triangle?
.
Let b = base
then
3b-10 = height
.
area = (1/2)base*height
156 = (1/2)b(3b-10)
312 = b(3b-10)
312 = 3b^2-10b
0 = 3b^2-10b-312
solve using the quadratic formula to get:
x = {12, -8.67}
throw out the negative solution leaving
x = 12 inches
.
details of quadratic formula follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-10x%2B-312+=+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=%28-10%29%5E2-4%2A3%2A-312=3844.

Discriminant d=3844 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+3844+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+3844+%29%29%2F2%5C3+=+12
x%5B2%5D+=+%28-%28-10%29-sqrt%28+3844+%29%29%2F2%5C3+=+-8.66666666666667

Quadratic expression 3x%5E2%2B-10x%2B-312 can be factored:
3x%5E2%2B-10x%2B-312+=+3%28x-12%29%2A%28x--8.66666666666667%29
Again, the answer is: 12, -8.66666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-10%2Ax%2B-312+%29