Chapter 6.5, Problem 14E

To determine

To calculate: The distance

  $AB$ across the river.

Answer to Problem 14E

Length of $AB=36\text{ ft}$

Explanation of Solution

Given information:

The following figure:

  

  $△ABC\sim △DEC$

To find $AB$ , write and solve a proportion.

  $\begin{array}{l}\frac{AB}{DE}\text{=}\frac{AC}{DC}\text{ [Write Proportion]}\\ \frac{AB}{24}\text{=}\frac{30}{20}\text{ [Substitute values]}\\ \frac{AB}{24}\text{=}\frac{3}{2}\text{ [Divide out common factors]}\\ AB\cdot 2=3\cdot 24\text{ [Form cross product]}\\ AB\cdot 2=72\text{ [Multiply]}\\ AB=36\text{ [Divide both sides by 2] }\end{array}$

Therefore,

  $AB=36\text{ ft}$ .