Question #d2ca6

1 Answer
Dec 4, 2016

$b = \frac{2 A}{9} - 35 = \frac{2}{9} A - 35$

Explanation:

The formula for the area of a trapezois is $A = \frac{\left({b}_{1} + {b}_{2}\right) h}{2}$,

where ${b}_{1}$ and ${b}_{2}$ are the lengths of the bases and $h$ is the height.

In this example,

$A = \frac{9 \left(b + 35\right)}{2}$, find $b$

$2 \cdot A = \frac{9 \left(b + 35\right)}{\cancel{2}} \cdot \cancel{2} \textcolor{w h i t e}{a a a}$Multiply both sides by 2

$2 A = 9 \left(b + 35\right)$

$\frac{2 A}{9} = \frac{\cancel{9} \left(b + 35\right)}{\cancel{9}} \textcolor{w h i t e}{a a a}$Divide both sides by 9

$\frac{2 A}{9} \textcolor{w h i t e}{a a} = b + 35$

$\textcolor{w h i t e}{a} - 35 \textcolor{w h i t e}{a a a} - 35 \textcolor{w h i t e}{a a a}$Subtract 35 from both sides

$\frac{2 A}{9} - 35 = b$

This can also be written as $b = \frac{2}{9} A - 35$