What Is The Height Of This Triangle?

Question

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?

I have to show work, I'm not asking you to do it FOR me, but some help would be fantastic. The choices are:

A) 7/2 Units
B) -5 + Square Root of 193 over 4 units.
C) 5 + Square Root of 193 over 2 units.
D) 12 Units

Answer 1

Draw out your triangle!

The base is x, and the height is 2x+5 (because the question said the height was five more than twice the base).

You know that the area of a triangle is 1/2(base)(height), so plug in what you have:
1/2(x)(2x+5) = 21 (because the area must be 21).

Now solve!!

[Hint: You can make the equation quadratic (remember: 0 = #x^2 +#x +#), and then use the quadratic formula to solve... That's just one way to do it]

Answer 2

12