Question

a pair of similar figures is given below. (note: the figures are not drawn to scale.) the sides bc and de are corresponding sides. use the information below to find the area of figure 1 and the perimeter of figure 2.

figure 1
area of figure 1 = m²
perimeter of figure 1 = 36 m
bc = 6 m

figure 2
area of figure 2 = 150 m²
perimeter of figure 2 = m
de = 5 m

Explanation:

Step1: Find the ratio of the side - lengths

The ratio of the side - lengths of two similar figures is given by $\frac{BC}{DE}$. Given $BC = 6m$ and $DE=5m$, the ratio of the side - lengths $k=\frac{BC}{DE}=\frac{6}{5}$.

Step2: Find the ratio of the areas

For two similar figures, the ratio of their areas is $k^{2}$. So, $\frac{A_1}{A_2}=k^{2}=(\frac{6}{5})^{2}=\frac{36}{25}$, where $A_1$ is the area of Figure 1 and $A_2 = 150m^{2}$ is the area of Figure 2. Then $A_1=\frac{36}{25}\times A_2$. Substituting $A_2 = 150m^{2}$, we get $A_1=\frac{36}{25}\times150 = 216m^{2}$.

Step3: Find the ratio of the perimeters

For two similar figures, the ratio of their perimeters is equal to the ratio of their corresponding side - lengths. Let $P_1 = 36m$ be the perimeter of Figure 1 and $P_2$ be the perimeter of Figure 2. Then $\frac{P_1}{P_2}=\frac{BC}{DE}=\frac{6}{5}$. Cross - multiplying gives $P_2=\frac{5}{6}\times P_1$. Substituting $P_1 = 36m$, we get $P_2=\frac{5}{6}\times36=30m$.

Answer:

Area of Figure 1: $216m^{2}$
Perimeter of Figure 2: $30m$