Chapter 11.5, Problem 2BCYP

To determine

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

Answer to Problem 2BCYP

The scale factor is $k=\frac{40}{16}$ and the value of $x=16\text{mm}$ .

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.

As both the figure are similar then,

  $\begin{array}{l}{\left(\frac{40\text{mm}}{x\text{mm}}\right)}^2=\frac{400{\text{mm}}^2}{64{\text{mm}}^2}\\ x^2=\left(1600\text{mm}\right)\frac{64{\text{mm}}^2}{400{\text{mm}}^2}\\ x^2=64{\text{mm}}^2\left(4\right)\\ x=16\text{mm}\end{array}$

Then, the scale factor is,

  $k=\frac{40}{16}$