Question

The ratio of the perimeters of two similar triangles is 4:7. What is the area of each of these triangles if the sum of their areas is 65cm2.

Answer 1

Answer: 49 cm² and 16 cm²

Explanation:

1. If the triangles are similar and the ratio of the perimeter os 4:7, then the areas are in the following ratio:

`4^(2):7^(2)\\16:49`

2. You know that the sum of their areas is 65 cm², then, you can calculate the area of the larger triangle as following:

`A_1=65((49)/(49+16))=49cm^(2)`

3. The area of the smaller triangle is:

`A_2=65((16)/(49+16))=16cm^(2)`