Question

a pair of similar figures is given below. (note: the figures are not drawn to scale.)
the sides \\(\overline{wx}\\) and \\(\overline{yz}\\) are corresponding sides.

use the information below to find \\(wx\\) in figure 1 and the perimeter of figure 2.

figure 1	figure 2
perimeter of figure 1: \\(24\\,\text{m}\\)	perimeter of figure 2: \\(\square\\,\text{m}\\)
\\(wx = \square\\,\text{m}\\)	\\(yz = 5\\,\text{m}\\)

Explanation:

Step1: Find area scale factor

$\text{Area scale factor} = \frac{\text{Area of Figure 2}}{\text{Area of Figure 1}} = \frac{150}{96} = \frac{25}{16}$

Step2: Find linear scale factor

$\text{Linear scale factor} = \sqrt{\frac{25}{16}} = \frac{5}{4}$
This is the ratio of Figure 2 to Figure 1.

Step3: Calculate length $WX$

Since $\frac{YZ}{WX} = \frac{5}{4}$, rearrange to solve for $WX$:
$WX = YZ \times \frac{4}{5} = 5 \times \frac{4}{5} = 4$

Step4: Calculate perimeter of Figure 2

$\text{Perimeter of Figure 2} = \text{Perimeter of Figure 1} \times \frac{5}{4} = 24 \times \frac{5}{4} = 30$

Answer:

$WX = 4$ m
Perimeter of Figure 2 = 30 m