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