Chapter 7.2, Problem 26PPS

To determine

To find: The perimeter of the $\Delta DEF$ .

Answer to Problem 26PPS

The perimeter of $\Delta DEF$ is $20.25$ unit.

Explanation of Solution

Given:

The given figure is as:

  

  $\Delta DEF\sim \Delta CBF$ .

The perimeter of $\Delta CBF$ is $27$ & $DF=6,FC=8$ .

Calculation:

Two polygons are similar if their corresponding angles are congruent and the corresponding sides have a constant ratio.

As the given two triangles are similar so ratio of corresponding sides is constant.

The ratio of the corresponding side of the smaller triangle to the larger triangle is,

  $\begin{array}{c}r=\frac{DF}{FC}\\ =\frac{6}{8}\\ =\frac{3}{4}\end{array}$

The perimeter of $\Delta DEF$ is calculated as:

  $\begin{array}{c}\text{Perimeter of }\Delta DEF=\frac{3}{4}\cdot 27\left[\begin{array}{l}\text{Multiply the perimeter of larger triangle by the ratio to get}\\ \text{ the perimeter of smaller triangle}\end{array}\right]\\ =20.25\end{array}$

The perimeter of $\Delta DEF$ is $20.25$ unit.

Therefore the perimeter of $\Delta DEF$ is $20.25$ unit.