Question

The ratio of the perimeters of two similar triangles is 2:3, the sum of their areas is 260 cm2. What are the areas of each of these triangles?

Answer 1

80 cm², 180 cm²

Explanation:

The ratio of areas is the square of the ratio of perimeters:

2²:3² = 4:9

The sum of these "ratio units" is 4+9 = 13, corresponding to a sum of areas of 260 cm². Hence each "ratio unit" represents (260 cm²)/13 = 20 cm². Then the two areas are ...

• 4×20 cm² = 80 cm²

• 9×20 cm² = 180 cm²