Question

Question 9
The ratio of the corresponding altitudes of two similar triangles is 3 : 5. Is it correct to say that ratio of their areas is 6 : 5? Why?

Answer 1

False

By the property of two similar triangles,

$\left(\frac{Are{a}_1}{Are{a}_2}\right)={\left(\frac{Altitud{e}_1}{Altitud{e}_2}\right)}^2$

$\Rightarrow \left(\frac{Are{a}_1}{Are{a}_2}\right)={\left(\frac{3}{5}\right)}^2$ $[\because \frac{Altitud{e}_1}{Altitud{e}_2}=\frac{3}{5},given]$

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

So, the given statement is not correct.