# What is the height of a triangle with an area of 10 square inches and a base of 5 inches?

Sep 8, 2015

The height is $4$ inches.

#### Explanation:

For a triangle, we have Area = $\frac{1}{2}$ base times height.

With $a$ = area, $b$ = base and $h$ = height, we have:

$A = \frac{1}{2} b h$

We are told that $A = 10$ square inches and $b = 5$ inches, so we need to solve (find $h$) for:

$10 = \frac{1}{2} \left(5\right) h$

We can get rid of the fraction by multiplying by $2$ on both sides:

$20 = 5 h$ Now divide noth sides by $5$ (or multiply by $\frac{1}{5}$, to get

$\frac{20}{5} = \frac{5 h}{5}$ so $4 = h$

The height is $4$ inches.