SOLUTION: Designing tents. THe length of the base of the triangular sheet of canvas above the door of the tent shown below is 2 feet more than twice its height. The area is 30 square feet.

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Question 592176: Designing tents. THe length of the base of the triangular sheet of canvas above the door of the tent shown below is 2 feet more than twice its height. The area is 30 square feet. Find the height and the length of the base of the triangle.
I am having problems on how to set this up
Thank you
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
THe length of the base of the triangular sheet of canvas above the door of the tent shown below is 2 feet more than twice its height. The area is 30 square feet. Find the height and the length of the base of the triangle.
.
Let h = height
then
h+2 = base
.
since area of any triangle is
(1/2)base*height
we have
(1/2)h(h+2) = 30
h(h+2) = 60
h^2 + 2h = 60
h^2 + 2h - 60= 0
since you can't factor you must apply the quadratic equation to get:
h = {6.8, -8.8}
throw out the negative solution leaving:
h = 6.8 feet
.
details of quadratic follows:
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=244 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 6.81024967590665, -8.81024967590665. Here's your graph:
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