## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$h=\dfrac{2A}{a+b}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $A=\dfrac{1}{2}ah+\dfrac{1}{2}bh$ for $h ,$ use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Using the properties of equality to isolate the variable, the equation above is equivalent to \begin{array}{l}\require{cancel} A=\dfrac{1}{2}ah+\dfrac{1}{2}bh \\\\ 2(A)=2\left( \dfrac{1}{2}ah+\dfrac{1}{2}bh \right) \\\\ 2A=ah+bh \\\\ 2A=h(a+b) \\\\ \dfrac{2A}{a+b}=\dfrac{h(a+b)}{a+b} \\\\ \dfrac{2A}{a+b}=h \\\\ h=\dfrac{2A}{a+b} .\end{array}