Chapter 6, Problem 49SGR

To determine

To calculate:Tofind the distance across the pond.

Answer to Problem 49SGR

Distance across the pond is $70$ m

Explanation of Solution

Given information: $\Delta ABE\approx \Delta ACD$ in below figure

  

Calculation:

Figure is given as

  

Here, $\Delta ABE\approx \Delta ACD$

Since the above triangles are similar, hence the corresponding sides are proportional

  $\frac{BE}{CD}=\frac{AB}{AC}$

On substituting the values in above proportion

  $\frac{44}{d}=\frac{110}{110+65}$

On solving the above proportion,

  $\begin{array}{l}\frac{44}{d}=\frac{110}{175}\\ 44\times 175=110\times d\\ 110\times d=44\times 175\\ d=\frac{44\times 175}{110}\\ d=\frac{2\times 175}{5}\\ d=\frac{2\times 35}{1}\\ d=70\end{array}$

Hence, distance across the pond is $70$ m