SOLUTION: the base of a triangle is 5cm greater than height. The area is 33cm^2. Find the height and length of the base.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: the base of a triangle is 5cm greater than height. The area is 33cm^2. Find the height and length of the base.      Log On


   

Question 135631: the base of a triangle is 5cm greater than height. The area is 33cm^2. Find the height and length of the base.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a triangle is given by A=%281%2F2%29bh where b is the measure of the base and h is the measure of the height.

You are given that the base is 5 cm longer than the height, so b=h%2B5

You can substitute this expression for b into the equation for the area:

%281%2F2%29%28h%2B5%29%28h%29, and set that equal to the given area:

%281%2F2%29%28h%2B5%29%28h%29=33

Solve the equation for h giving you part of the answer, then add 5 to the solution to get b. Remember that since you will be solving a quadratic equation, you will get two roots. One of the roots in this case will be negative which makes no sense when solving for a length measurement. So exclude the negative root and the positive root will be your solution (the value for h)