Chapter 6.7, Problem 25STP

To determine

To find: The perimeter of the triangle DEF, that is similar to triangle LMN by the scale factor $\frac{1}{3}$ .

Answer to Problem 25STP

Required perimeter of triangle DEF is 8 centimeters.

Explanation of Solution

Given information: Two similar triangles DEF and LMN and perimeter of triangle LMN is given 24 centimeter, and scale factor relation triangle LMN to triangle DEF is 1/3.

Concept used:

In similar triangles, scale factor is actually the ratio of their corresponding sides. That means each side of triangle DEF is one-third of its corresponding sides. Thus, its perimeter of triangle DEF would also be one-third of perimeter of triangle LMN.

Calculation:

Perimeter of triangle DEF is calculated as follows:

  $\begin{array}{c}\text{perimeter of triangle }DEF=\frac{1}{3}\times \text{perimeter of triangle}LMN\\ =\frac{1}{3}\times 24\\ =8\text{centimeter}\end{array}$

Based on above calculation, required perimeter of triangle DEF is 8 centimeters.