Question

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

image of two similar triangles, larger green triangle with a labeled side of 6 m and perimeter ( p_1 = 24 ) m, smaller blue triangle with a corresponding labeled side of 1 m and perimeter ( p_2 = ? )

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

Explanation:

Step1: Find the scale factor

The ratio of corresponding sides is $\frac{1}{6}$ (since the smaller side is 1 m and the corresponding larger side is 6 m).

Step2: Use the scale factor for perimeters

For similar figures, the ratio of perimeters is equal to the ratio of corresponding sides. So, $P_2 = P_1\times\frac{1}{6}$. Substituting $P_1 = 24$ m, we get $P_2 = 24\times\frac{1}{6} = 4$ m.

Answer:

4