SOLUTION: Hello, I was wondering if you would be able to help me out on this problem. I'm not sure where to start: Use the given area to find the height and base of the triangle.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hello, I was wondering if you would be able to help me out on this problem. I'm not sure where to start: Use the given area to find the height and base of the triangle.       Log On


   

Question 442578: Hello,
I was wondering if you would be able to help me out on this problem. I'm not sure where to start:
Use the given area to find the height and base of the triangle.
Area = 84
Base = 2x+5
Height = x
Then I need to type an integer or a simplified fraction for what the height of the triangle is
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Recall that %281%2F2%29%2Ab%2Ah+=+A
We are given that b+=+2x%2B5 and h+=+x and A=84
Then
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B5x%2B-168+=+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=%285%29%5E2-4%2A2%2A-168=1369.

Discriminant d=1369 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+1369+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+1369+%29%29%2F2%5C2+=+8
x%5B2%5D+=+%28-%285%29-sqrt%28+1369+%29%29%2F2%5C2+=+-10.5

Quadratic expression 2x%5E2%2B5x%2B-168 can be factored:
2x%5E2%2B5x%2B-168+=+2%28x-8%29%2A%28x--10.5%29
Again, the answer is: 8, -10.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B5%2Ax%2B-168+%29


So our positive answer is x = 8. This means our height is 8.
What is left to find is the base.
Remember, our base = 2x+5, so plug in x=8 to find the base.
cartoon%28b+=+2%288%29+%2B+5+=+21%2C+b+=+highlight%2821%29%29
So our base is highlight%2821%29
and our height is highlight%288%29