# How do you solve A=h/2(a+b) for h?

Mar 5, 2018

See a solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{2}$ to eliminate the fraction while keeping the equation balanced:

$\textcolor{red}{2} \times A = \textcolor{red}{2} \times \frac{h}{2} \left(a + b\right)$

$2 A = \cancel{\textcolor{red}{2}} \times \frac{h}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} \left(a + b\right)$

$2 A = h \left(a + b\right)$

Now, divide each side of the equation by $\textcolor{red}{a + b}$ to solve for $h$ while keeping the equation balanced:

$\frac{2 A}{\textcolor{red}{a + b}} = \frac{h \left(a + b\right)}{\textcolor{red}{a + b}}$

$\frac{2 A}{a + b} = \frac{h \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(a + b\right)}}}}{\cancel{\textcolor{red}{a + b}}}$

$\frac{2 A}{a + b} = h$

$h = \frac{2 A}{a + b}$