Question

the figures below are similar. the labeled sides are corresponding.

(image of two similar triangles: smaller blue triangle with base 2 m, perimeter ( p_1 = 7 ) m; larger purple triangle with base 8 m, perimeter ( p_2 = ? ))

what is the perimeter of the larger triangle?
( p_2 = square ) meters

Explanation:

Step1: Find the scale factor

The scale factor \(k\) is the ratio of the corresponding sides. Given the side of the smaller triangle is \(2\) m and the corresponding side of the larger triangle is \(8\) m. So, \(k=\frac{8}{2}=4\).

Step2: Calculate the perimeter of the larger triangle

Since the ratio of perimeters of similar figures is equal to the scale factor. Let \(P_1 = 7\) m (perimeter of the smaller triangle) and \(P_2\) be the perimeter of the larger triangle. Using the formula \(P_2=k\times P_1\). Substitute \(k = 4\) and \(P_1=7\) into the formula: \(P_2=4\times7\).

Answer:

\(28\) meters