The perimeters of two similar triangles are 36 cm and 24 cm, respectively. Find the ratio of their areas.
Answer & explanation
Correct answer: option 3
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