The perimeters of 2 similar triangles are 18 and 36 and the sum of their areas is 30, find the area of the larger triangle.

Let the perimeter of the first triangle be P1 = 18 cm, and the perimeter of the second triangle is P2 = 36 cm.

The ratio of the perimeters of similar triangles is equal to the coefficient of their similarity.

K = P1 / P2 = 18/36 = 1/2.

The ratio of the areas of such polyhedra is equal to the squared coefficient of their similarity.

S1 / S2 = K2 = 1/4.

4 * S1 = S2.

By condition, S1 + S2 = 30 cm2.

S1 = 30 – S2.

4 * (30 – S2) = S2.

5 * S2 = 120.

S2 = 120/5 = 24 cm2.

S1 = 30 – 24 = 6 cm2.

Answer: The areas are 6 cm2 and 24 cm2.