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?

1 Answer
May 11, 2018

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