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 ?

Answer 1

False: If two triangles are similar, then the ratio of areas of two triangles will be equal to the square of the ratio of their corresponding sides or altitudes or angle bisectors.

If $\Delta ABC\sim \Delta PQR$, then

Refer image,

$\frac{ar\left(\Delta ABC\right)}{ar\left(\Delta PQR\right)}={\left(\frac{AD}{PM}\right)}^2$ (By area theorem)

$\Rightarrow \frac{ar\left(\Delta ABC\right)}{ar\left(\Delta PQR\right)}={\left(\frac{3}{5}\right)}^2$

$=\frac{9}{25}\ne \frac{6}{5}$

So, the given statement is false.