Question

exit ticket: two polygons, polygon a and polygon b, are similar. the side lengths of polygon a are 4 cm, 5 cm, and 6 cm, and the corresponding side lengths of polygon b are 8 cm, 10 cm, and 12 cm. a. what is the scale factor from polygon a to polygon b? b. if the perimeter of polygon a is 15 cm, what is the perimeter of polygon b?

Explanation:

Step1: Find the scale - factor formula

For similar polygons, the scale factor $k$ from polygon A to polygon B for corresponding sides is given by the ratio of corresponding side lengths. Let's take one pair of corresponding sides. If a side of polygon A is $a$ and the corresponding side of polygon B is $b$, then $k=\frac{b}{a}$. Taking the sides of length 4 cm in polygon A and 8 cm in polygon B, $k = \frac{8}{4}=2$.

Step2: Use the perimeter - scale factor relationship

The ratio of the perimeters of two similar polygons is equal to the scale factor. Let $P_A$ be the perimeter of polygon A and $P_B$ be the perimeter of polygon B. Then $\frac{P_B}{P_A}=k$.
We know that $P_A = 15$ cm and $k = 2$ from step 1.
So $P_B=k\times P_A$.
$P_B=2\times15 = 30$ cm.

Answer:

a. The scale factor from Polygon A to Polygon B is 2.
b. The perimeter of Polygon B is 30 cm.