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)   (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 (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=3844 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 12, -8.66666666666667. Here's your graph:
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