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 and area of the smaller triangle.

Answer 1

32 m, 80 m^2

Explanation:

Ratio of their sides = 12 : 8 = 3 : 2

Ratio of their perimeter = 3 : 2

so 48 : perimeter of smaller triangle = 3 : 2

Perimeter of smaller triangle = 48 * 2 / 3 = 32 m

Ratio of their areas = 3^2 : 2^2 = 9 : 4

so 180 : area of smaller triangle = 9 : 4

Area of smaller triangle = 180 * 4 / 9 = 80 m^2