Chapter 11.5, Problem 4CYU

To determine

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

Answer to Problem 4CYU

The value of the scale factor is $\frac{3}{4}$ and the value of $x=35\text{cm}$ .

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,

  $\begin{array}{l}{\left(\frac{15}{x}\right)}^2=\frac{153}{272}\\ x^2={\left(15\right)}^2\frac{272}{153}\\ x^2=400\\ x=20\text{in}\end{array}$

Then, the scale factor is,

  $\begin{array}{c}k=\frac{15}{x}\\ =\frac{15}{20}\\ =\frac{3}{4}\end{array}$