Chapter 7, Problem 1STP

To determine

Find the approximate width of the ravine.

Answer to Problem 1STP

D

Explanation of Solution

Given:

A wants to measure the width of a ravine. He marks distances as shown in the diagram.

  

Calculation:

Consider $\Delta ABC\text{ and }\Delta EDC$ :

  $\begin{array}{l}m\angle ABC=m\angle EDC=90°\\ m\angle ACB=m\angle ECD\mathrm{............}[\text{vertically opposite angles]}\end{array}$

So, by AA Similarity , $\Delta ABC\sim \Delta EDC$ .

Hence ,

  $\begin{array}{l}\frac{AB}{ED}=\frac{BC}{DC}\\ \Rightarrow \frac{AB}{10}=\frac{18}{22.5}\\ \Rightarrow AB=10\cdot \frac{18}{22.5}\mathrm{..................}[\text{multiply each side by 10]}\\ \Rightarrow AB=8\end{array}$

So, the width of Ravine is 8 ft.

Hence , the correct option is D.