Question

two polygons are similar. the perimeter of the smaller polygon is 48 centimeters and the ratio of the corresponding side lengths is \\(\frac{2}{3}\\). find the perimeter of the other polygon.\
the perimeter of the other polygon is \\(\square\\) centimeters.

Explanation:

Step1: Identify ratio type

The ratio $\frac{2}{3}$ is smaller polygon : larger polygon.

Step2: Set up perimeter proportion

Let $P$ = perimeter of larger polygon.
$\frac{48}{P} = \frac{2}{3}$

Step3: Solve for $P$

Cross-multiply: $2P = 48 \times 3$
Calculate right-hand side: $2P = 144$
Isolate $P$: $P = \frac{144}{2} = 72$

Answer:

72