Chapter 11.5, Problem 10PPS

To determine

To find: The scale factor and the value of $x$ .

Answer to Problem 10PPS

The value of the scale factor is $\frac{5}{6}$ and the value of $x=10\text{m}$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Two polygons are similar only when the corresponding angles are equal and congruent and corresponding side length are in proportion.

Consider the formula to determine the scale factor is,

  $k^2=\frac{A_1}{A_2}$

As both the figure are similar then,

  $\begin{array}{l}{\left(\frac{x}{12\text{m}}\right)}^2=\frac{50}{72}\\ x^2={\left(12\text{m}\right)}^2\frac{50}{72}\\ x^2=100\\ x=10\text{m}\end{array}$

Then, the scale factor is,

  $\begin{array}{c}k=\frac{x}{12}\\ =\frac{10}{12}\\ =\frac{5}{6}\end{array}$