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 solve for $P_l$:
$P_l = P_s \times \frac{4}{3}$
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