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.

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) (Show Source): You can put this solution on YOUR website!
Recall that
We are given that and and
Then

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1369 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 8, -10.5. Here's your graph:

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.

So our base is
and our height is

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