Question

Question #cbd7c

Answer 1

Area of `Δ_1` = `27 cm^2` and Area of `Δ_2` = `48 cm^2`

Explanation:

Given that the perimeters of two similar triangles `Δ_1` and `Δ_2`
, is in the ratio `3 : 4`. The sum of their areas is `75 cm^2`.

Since the the perimeters are similar and in the ratio of `3 : 4`, all their sides will be in the ratio of `3 : 4` and the area will be in the ratio of the squares of the sides i.e. `3^2 : 4^2` => `9:16`

Let area of `Δ_1` will `9a`. Area of `Δ_2` is `16a`

`9a + 16a = 75 cm^2`

=> `25a = 75 cm^2`

=> `a = 3 cm^2`

Area of `Δ1` = `9*3 cm^2` = `27 cm^2`

Area of `Δ2` = `16*3 cm^2` = `48 cm^2`