Question

Two similar triangles have a pair of corresponding sides of length 12 meters and 8 meters. The larger triangle has a perimeter of 48 meters and an area of 180 square meters. Find the perimeter P and area A of the smaller triangle.

Answer 1

Since S2/S1 = 8/12 = 2/3,
P2/P1 = 2/3
A2/A1 = (2/3)^2

Answer 2

the side length of the smaller triangle is 2/3 that of the larger triangle

so the perimeter of the smaller triangle is 2/3 the perimeter of the larger triangle

and the area of the smaller triangle is (2/3)^2 the area of the larger triangle