Chapter 6.5, Problem 6E

To determine

To find $x$:

Answer to Problem 6E

The value of $x$ is 24in.

Explanation of Solution

Given information:

Consider the given triangles ABC and LMN

Where AC $=36in\text{ BC=24 }in\text{ LN=}x\text{ MN=16 }in$

And $\Delta ABC\sim \Delta LMN$

Calculation :

Since both the triangles are similar,then the ratio of their corresponding sides will also be equal.

  $\frac{AB}{LM}=\frac{BC}{MN}=\frac{AC}{LN}$

  $=\frac{36}{x}=\frac{24}{16}$

  $=>x=\frac{16\times 36}{24}$

  $x=24in$