Chapter 5.9, Problem 9IP

To determine

To find: The value of $LN$ if triangle $LMN$ is similar to triangle $RST$ .

Answer to Problem 9IP

Thevalue of $LN$ is 27 inches.

Explanation of Solution

Given information:

Triangle $LMN$ is similar to triangle $RST$ . The measure of the sides are $RT=9\text{in},MN=21\text{in}$ and $ST=7\text{in}$ .

Calculation:

Since triangle $LMN$ is similar to triangle $RST$ . So, their corresponding sides are proportional and $LN\sim RT$ and $MN\sim ST$ .

Let the measure of $LN$ is $x$ . Calculate the value of $x$ .

  $\frac{LN}{RT}=\frac{MN}{ST}$

Substitute the values in the above expression.

  $\begin{array}{c}\frac{x}{9}=\frac{21}{7}\\ x=\frac{21}{7}\times 9\\ x=3\times 9\\ x=27\end{array}$

Therefore, the value of $LN$ is 27 inches.