Question

The perimeters of two similar triangles is in the ratio 3:4. The sum of their areas is 75 sq cm. What is the area of the smaller triangle?

Answer 1

`27` square centimeters

Explanation:

Perimeter is the sum of lengths of triangles. Hence its unit in `cm`. Area has unit `cm^2` i.e. length squared. So if lengths are in ratio `3:4`, areas are in ratio `3^2:4^2` or `9:16`. This is because the two triangles are similar.

As total area is `75` square centimeters, we need to divide it in ratio `9:16`, of which first will be area of smaller triangle.

Hence area of smaller triangle is `75xx9/(9+16)`

= `75xx9/25`

= `cancel75^3xx9/(cancel25^1)`

= `27` square centimeters

Area of larger triangle would be `75xx16/(9+16)=3xx16=48` square centimeters