Question:
The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively. Find the ratio of their areas.
Solution:
Given: The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively.
To find: Ratio of areas of triangle.
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding altitudes.
$\frac{\operatorname{ar}(\text { triangle } 1)}{\operatorname{ar}(\text { triangle } 2)}=\left(\frac{\text { altitude1 }}{\text { altitude } 2}\right)^{2}$
$\frac{\operatorname{ar}(\text { trianglel })}{\operatorname{ar}(\text { triangle } 2)}=\left(\frac{6}{9}\right)^{2}$
$\frac{a r(\text { trianglel })}{a r(\text { triangle } 2)}=\frac{4}{9}$