Question:
The ratio of the corresponding altitudes of two similar triangles is $\frac{3}{5}$. Is it correct to say that ratio of their areas is $\frac{6}{5}$ ? Why?
Solution:
False
By the property of area of two similar triangles,
$\left(\frac{\text { Area }_{1}}{\text { Area }_{2}}\right)=\left(\frac{\text { Altitude }_{1}}{\text { Altitude }_{2}}\right)^{2}$
$\Rightarrow$ $\left(\frac{\text { Area }_{1}}{\text { Area }_{2}}\right)=\left(\frac{3}{5}\right)^{2}$ $\left[\because \frac{\text { altitude }_{1}}{\text { altitude }_{2}}=\frac{3}{5}\right.$, given $]$
$=\frac{9}{25} \neq \frac{6}{5}$
So, given statement is not correct,