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

Step-by-step 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:

$A_1=65(\frac{49}{49+16})=49cm^{2}$

3. The area of the smaller triangle is:

$A_2=65(\frac{16}{49+16})=16cm^{2}$