Question

the figures below are similar. the labeled sides are corresponding.
7.4 m
3.3 m
$p_1 = ?$
$p_2 = 9.9$ m
what is the perimeter of the larger triangle?
$p_1 = \square$ meters

Explanation:

Step1: Find the scale factor

The ratio of corresponding sides of similar figures is equal to the ratio of their perimeters. Let the scale factor be \( k \), so \( k=\frac{7.4}{3.3} \).

Step2: Calculate the perimeter of the larger triangle

Since the ratio of perimeters is equal to the scale factor, we have \( P_1 = k\times P_2 \). Substitute \( k=\frac{7.4}{3.3} \) and \( P_2 = 9.9 \) into the formula: \( P_1=\frac{7.4}{3.3}\times9.9 \). First, simplify \( \frac{9.9}{3.3}=3 \), then \( P_1 = 7.4\times3 \).

Step3: Compute the result

\( 7.4\times3 = 22.2 \).

Answer:

22.2