The base of a triangle is 8 more than twice it’s height.

Question

If the area of the triangle is 51 square centimeters, find its base and height.

Answer 1

Area of triangle=1/2bh

b=2h+8

Substitute 2h+8 for b

solve for h

51=1/2(2h+8)h

51=h²+4h

We have a quadratic!

Subtract 51 from both sides

0=h²+4h-51

Since this equation cannot be factored, we must use the quadratic equation.

To save time, I'll use a calculator to determine the zeroes. Let me know if you need an explanation on how to use the quadratic formula to solve equations and I would be happy to go into more detail.

We find that h≈5.4162 and -9.4162.

We throw out the negative value because height is a scalar and therefore cannot be negative!

So, h=5.4162. In order to find the base, we do what the question tells us: The base is 8 more than twice the height.

b=2(5.4162)+8≈18.8324

You can check these answers by plugging them into A=1/2bh.

Let me know if you have any questions.