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.

Part a) The area of the smaller triangle is  

Part b) The area of the larger triangle is  

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor and the ratio of its areas is equal to the scale factor squared

step 1

Find the scale factor

Let

z-----> the scale factor

------> ratio of corresponding perimeters

step 2

Find the area of each triangle

Let

z-----> the scale factor

x-----> the area of the smaller triangle

y-----> the area of the larger triangle

we know that

------> equation A

we have

substitute

------> equation B

substitute equation B in equation A and solve for y

Find the value of x

------>

b