The perimeters of two similar triangles are 36 cm and 24 cm, respectively. Find the ratio of their areas.

9 : 4

We have,

The perimeters of two similar triangles are 36 cm and 24 cm

We know that,

\(\frac{Perimeter1}{Perimeter2}\) = \(\frac{Side1}{Side2}\)

\(\frac{(Side1)^2}{(Side1)^2}\) = \(\frac{Area1}{Area2}\) 

According to the question,

\(\frac{36}{24}\) = \(\frac{Side1}{Side2}\)

= \(\frac{3}{2}\) = \(\frac{Side1}{Side2}\) 

So,

\(\frac{3^2}{2^2}\) = \(\frac{Area1}{Area2}\)

\(\frac{Area1}{Area2}\) = \(\frac{9}{4}\) = 9 : 4