Question

The ratio of the perimeters of two similar triangles is 4:3. What are the areas of these triangles if the sum of their areas is 130cm^2?

Answer 1

The areas of triangles are
`46.8\ cm^(2)` and
`83.2\ cm^(2)`

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

Let

z-------> the scale factor

x-----> the area of the larger triangle

y-----> the area of the smaller triangle

so

`z^(2)=(x)/(y)`

In this problem we have

`z=(4)/(3)`

`((4)/(3))^(2)=(x)/(y)`

`x=(16)/(9)y` ------> equation A

`x+y=130` ------> equation B

substitute equation A in equation B

`(16)/(9)y+y=130`

`(25)/(9)y=130`

`y=130*9/25=46.8\ cm^(2)`

Find the value of x

`x=(16)/(9)(46.8)=83.2\ cm^(2)`