Question #cbd7c

1 Answer
Jul 7, 2016

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