Chapter 8.5, Problem 11PSA

To determine

To find the perimeter of Trapezoid.

Answer to Problem 11PSA

The perimeter of Trapezoid is 51.

Explanation of Solution

Given information:

  $\overleftrightarrow{CD}$ is parallel to $\overleftrightarrow{BE}$

  $\begin{array}{l}AC=18,\\ AB=12,\\ AE=10,\\ CD=24\end{array}$

Formula used:

The below properties are used:

If the lines are parallel then their corresponding angles are congruent.

Corresponding sides of similar triangles are proportional.

Calculation:

  

It is given that,

  $\overleftrightarrow{CD}$ is parallel to $\overleftrightarrow{BE}$

  $\begin{array}{l}AC=18,\\ AB=12,\\ AE=10,\\ CD=24\end{array}$

  $\begin{array}{l}BC=AC-AB\\ =18-12\\ =6\end{array}$

If the lines are parallel then their corresponding angles are congruent.

  $\begin{array}{l}\angle ABE\cong \angle ACD\\ \angle AEB\cong \angle ADC\end{array}$

By AA similarity rule, we get

  $\Delta ABE~\Delta ACD$

Corresponding sides of similar triangles are proportional.

  $\begin{array}{l}\frac{AB}{BE}=\frac{AC}{CD}\\ \frac{12}{BE}=\frac{18}{24}\\ 18(BE)=288\\ \therefore BE=16\end{array}$

  $\begin{array}{l}\frac{AB}{BC}=\frac{AE}{ED}\\ \frac{12}{6}=\frac{10}{ED}\\ 12(ED)=60\\ \therefore ED=5\end{array}$

Perimeter $=(18-12)+16+(10-5)+24=51$