Chapter 11.7, Problem 30CCR

To determine

To find:Value of $x$ .

Answer to Problem 30CCR

Value of $x$ is $2.1$ km.

Explanation of Solution

Given information:

  $\Delta RSK$ is similar to $\Delta RUV$

  $\begin{array}{l}RK=2\\ RV=7.5\\ UV=8\\ SK=x\end{array}$

Given

  $\begin{array}{l}RK=2\\ RV=7.5\\ UV=8\\ SK=x\end{array}$

  $\Delta RSK$ is similar to $\Delta RUV$

When two figures are similar, the ratios of the lengths of their corresponding sides are equal.

Using above concept

We get

  $\frac{RK}{RV}=\frac{SK}{UV}=\frac{RS}{RU}$

Taking first two terms and substituting values

We get

  $\begin{array}{l}\frac{RK}{RV}=\frac{SK}{UV}\\ \Rightarrow \frac{2}{7.5}=\frac{x}{8}\\ \Rightarrow \left(7.5\right)x=2\left(8\right)\\ \Rightarrow \left(7.5\right)x=16\\ \Rightarrow \frac{\left(7.5\right)x}{7.5}=\frac{16}{7.5}\\ \Rightarrow x=\frac{16}{7.5}\\ \Rightarrow x=2.1\end{array}$

Therefore,

Value of $x$ is $2.1$ km.