The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively. Find the ratio of their areas.

Given:

The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively.

To do:

We have to find the ratio of their areas.

Solution:

We know that,

The ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding altitudes.

Therefore,

$ \begin{array}{l}
\frac{ar( triangle_{1})}{ar( triangle_{2})} =\left(\frac{altitude_{1}}{altitude_{2}}\right)^{2}\\
\\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\left(\frac{6}{9}\right)^{2}\\
\\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\left(\frac{2}{3}\right)^{2}\\
\\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\frac{4}{9}
\end{array}$

The ratio of areas of the two triangles is $4:9$.