SOLUTION: the base of a triangle is 5cm greater than the height. The area is 52^2. Find the height and the lenth of the base.

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Question 439695: the base of a triangle is 5cm greater than the height. The area is 52^2. Find the height and the lenth of the base.
Answer by asuar010(338)   (Show Source): You can put this solution on YOUR website!
first assign values to the base and the height of the triangle:
h=x
b=x+5
the formula of the area of a triangle is A=(1/2)b*h... so by substituting the values we get and simplifying this formula we get which becomes 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=21657 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 71.0815873707546, -76.0815873707546. Here's your graph:

so to get the values of the length and base of the triangle we add 5 to 71.08 so the real values are height=71.08 and base=76.08
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