Question

1. give the scale factor of figure a to figure b.
2. if the scale factor of figure a to figure b is 7:2, find the perimeter of figure a.

Explanation:

Step1: Calculate scale - factor for triangles

Find the ratio of corresponding sides. Let's take the ratio of the sides of length 15 in figure A and 7.2 in figure B. The scale factor $k$ is given by the ratio of the side - length of figure A to the side - length of figure B. So, $k=\frac{15}{7.2}=\frac{150}{72}=\frac{25}{12}$.

Step2: Calculate perimeter of figure B

For the trapezoid in figure B, the perimeter $P_B$ is the sum of its side - lengths. $P_B=12 + 9+9 + 5=35$.

Step3: Calculate perimeter of figure A

We know that the ratio of the perimeters of two similar figures is equal to the scale factor. Given the scale factor of figure A to figure B is $\frac{7}{2}$. Let the perimeter of figure A be $P_A$ and the perimeter of figure B be $P_B$. Then $\frac{P_A}{P_B}=\frac{7}{2}$. Since $P_B = 35$, we can solve for $P_A$: $P_A=\frac{7}{2}\times35=\frac{245}{2}=122.5$.

Answer:

1. Scale factor of figure A to figure B (triangles): $\frac{25}{12}$
2. Perimeter of figure A (trapezoids): $122.5$