The base of a triangle is 6 cm shorter than the altitude to that base. How do you find the length of the base and the altitude if the are of the triangle is 56 cm^2?
Let's approach this problem algebraically.
Assume that the triangle's altitude is
Then from the relationship between their lengths we can derive the following equation:
Since the area is given, the second equation is
All we have to do now is to solve this system of two equations with two unknowns.
Use an expression for
This is a quadratic equation, which in a more traditional form looks like
Its solutions are
Negative solution should be discarded since we are dealing with lengths, so the only solution for
Then the base