Question

two polygons are similar. the perimeter of the smaller polygon is 66 feet and the ratio of the corresponding side lengths is $\frac{3}{4}$. find the perimeter of the other polygon.
the perimeter of the other polygon is $square$ feet.

Explanation:

Step1: Relate perimeters to side ratio

For similar polygons, the ratio of perimeters equals the ratio of corresponding sides. Let $P_s = 66$ ft (smaller perimeter), $P_l$ = larger perimeter, ratio $\frac{P_s}{P_l} = \frac{3}{4}$.

Step2: Solve for larger perimeter

Rearrange the ratio to isolate $P_l$:
$$P_l = P_s \times \frac{4}{3}$$
Substitute $P_s = 66$:
$$P_l = 66 \times \frac{4}{3}$$

Step3: Calculate the value

$$66 \times \frac{4}{3} = 22 \times 4 = 88$$

Answer:

88