Chapter 7.5, Problem 30PPS

To determine

To find: The length of $BK$ .

Answer to Problem 30PPS

10 inches

Explanation of Solution

Given:

  

Distance between each shelve is 13 inches.

  $\overline{AK}$ is the median of $\Delta ABC$ .

  $EF$ is $3\frac{1}{3}$ inches.

In $\Delta ABC,\Delta ADF$ :

  $\angle D\cong \angle B$

  $\angle A$ is common to both the triangles.

By $A-A$ similarity:

  $\Delta ABC\sim \Delta ADF$

In similar triangles, corresponding sides are proportional to each other.

  $\begin{array}{l}\frac{AD}{AB}=\frac{DF}{\text{}BC}\\ \Rightarrow \frac{13}{3\times 13}=\frac{2\times 3\frac{1}{3}}{\text{}2\times BK}\\ \Rightarrow BK=10\end{array}$

  $BK$ is 10 inches.