SOLUTION: the base of a triangle is 5 cm greater than the height, the area is 33 cm^2, what is the height and length of the base, can you walk me through this? thanks so much

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Question 242114: the base of a triangle is 5 cm greater than the height, the area is 33 cm^2, what is the height and length of the base, can you walk me through this? thanks so much
Answer by solver91311(16868) About Me  (Show Source):
You can put this solution on YOUR website!

Let represent the measure of the base. Let represent the measure of the height.

We are given that

The area of a triangle is given by

But since we know the value of in terms of , we can write an equation for the area as a function of the height:



But since we are given the area, we can write:



Simplify and put into standard form:



Now all that is left is to solve the factorable quadratic and select the positive root for the measure of the height. The measure of the base then follows directly.

John