Chapter 11.5, Problem 12PPS

To determine

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

Answer to Problem 12PPS

The value of the scale factor is $\frac{3}{7}$ and the value of $x=6\text{ft}$ .

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,

  $\begin{array}{l}{\left(\frac{x}{14}\right)}^2=\frac{27}{147}\\ x^2={\left(14\right)}^2\frac{27}{147}\\ x^2=36\\ x=6\text{ft}\end{array}$

Then, the scale factor is,

  $\begin{array}{c}k=\frac{x}{14}\\ =\frac{6}{14}\\ =\frac{3}{7}\end{array}$