Chapter 8.5, Problem 27PSC

To determine

To find the length of the side.

Answer to Problem 27PSC

The length of the side is 8.75 m.

Explanation of Solution

Given information:

Two flagpoles are 10 m and 70 m tall and are 100 m apart.

Formula used:

The below property is used:

Corresponding sides of congruent triangles are proportional.

Calculation:

  

Let, $FB=x$ so

  $\begin{array}{l}AF=100–x,\hfill \\ EF=y\hfill \end{array}$

In ΔABC and ΔFBE,

  $\begin{array}{l}\frac{x}{100}=\frac{y}{10}\\ 10x=100y\\ 7(10x)=7(100y)\\ 70x=700y----Equation1\end{array}$

In ΔABD and ΔAFE,

  $\begin{array}{l}\frac{100-x}{100}=\frac{y}{70}\\ 7000-70x=100y----Equation2\end{array}$

Solving Equation 1 and Equation 2, we get

  $\begin{array}{l}7000-700y=100y\\ 800y=7000\\ y=\frac{7000}{800}\\ =8.75m\end{array}$