Chapter 1.7, Problem 47WE

To determine

To calculate:

Value of remaining variable $\left(b_1\right)$ .

Answer to Problem 47WE

Value of remaining variable $\left(b_1\right)$ is $28$ .

Explanation of Solution

Given information:

  $\begin{array}{l}A=\frac{h}{2}\left(b_1+b_2\right)\\ A=100\\ h=5\\ b_2=12\end{array}$

Calculations:

Area of trapezoid is,

  $A=\frac{h}{2}\left(b_1+b_2\right)$

Now substitute the $100$ for $A$ , and $5$ for $h$ , $12$ for $b_2$ .

  $100=\frac{5}{2}\left(b_1+12\right)$

Clear the parentheses using the distributive property.

  $100=\frac{5}{2}{b}_1+30$

Solve for variable $b_1$

Subtract $30$ from both sides,

  $\begin{array}{l}100-30=\frac{5}{2}{b}_1+30-30\\ 70=\frac{5}{2}{b}_1\end{array}$

Multiply each side by $\frac{2}{5}$ to solve for $b_1$

  $\begin{array}{l}70.\frac{2}{5}=\frac{5}{2}{b}_1.\frac{2}{5}\\ 28=b_1\end{array}$

Use the symmetry property,

Thus, $b_1=28$