SOLUTION: The height of a right triangle is 5 units more than twice its base. If the area of the triangle is 21 square units, what is its height?

Question 746903: The height of a right triangle is 5 units more than twice its base. If the area of the triangle is 21 square units, what is its height?

Answer by timvanswearingen(106) (Show Source): You can put this solution on YOUR website!
Let x represent the length of the base.
Then the height can be represented as (5 units more than twice the base)
Now, the formula for the area of a triangle is
So,
Using the distributive property,

Subtract 21 from both sides,

Now, using a=1, b=5/2, and c=-21, plug into the quadratic formula.

There are two possible answers. or
The second answer would result in a negative number. Since we are trying to find out the length of the base of a triangle, we can throw out the negative answer.
Thus,
So x is about 3.925 units.
x was representing the base. Since the height was 2x+5, simply plug in the x value found above to find the height.

h=12.850 units

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