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.

Hence the area of each of the triangles are:

49 cm^2 and 16 cm^2.

Step-by-step explanation:

If the two triangles are similar; the perimeters of the two triangles are in the same ratio as the sides.

We are given that the ratio of the perimeters of two similar triangles is 4:7.

Let a and b denotes  perimeter of two triangles.

i.e. here a:b=4:7.

Let A and B denote the area of two triangles.

also we know that for two similar triangles;

Hence,

Also the sum of their areas is 65 cm^2.

i.e.

on putting equation (2) in equation (1) we have:

49(65-B)=16B

49×65-49B=16B

49×65=49B+16B

49×65=65B

B=49 cm^2

Hence by equation (2) we have:

A=65-B

A=65-49=16 cm^2.

Hence the area of each of the triangles are:

49 cm^2 and 16 cm^2.

the answer to the expression is 83