Chapter 6.9, Problem 11PPS

To determine

In calculate: The distance d between two points A and B that is the width of key in basketball game.

Answer to Problem 11PPS

Key AB is 12 feet wide.

Explanation of Solution

Given information:

In a basketball game, the distance between Divon and Josh is 16 feet ,and between Devon and Macro is $5\frac{1}{3}=\frac{16}{3}$ feet and distance of Macro from key points A and B is 4 feet each as shown in given figure :

  

Concept used:

As both triangles are similar, ratios of their corresponding sides will be proportional, so

  $\frac{\text{Distance between A and B}}{\text{Distance between Josh and Devon}}=\frac{\text{Distance between B and Marco}}{\text{Distance between Marco and Devon}}$

Calculation: On plug in all related given values in above ratios:

  $\begin{array}{c}\frac{\text{d}}{16}=\frac{4}{\frac{16}{3}}\\ \frac{\text{d}}{16}=\frac{4\times 3}{16}\\ d=2\end{array}$

By above calculation, the distance between points A and B is 12 feet of key is 12 feet wide.