Triangles ABC and DEF are similar.
If $AC\ =\ 19\ cm$ and $DF\ =\ 8\ cm$, find the ratio of the area of two triangles.
"

Given:

 

Triangles ABC and DEF are similar.

 

$AC\ =\ 19\ cm$ and $DF\ =\ 8\ cm$.

To do:

 

We have to find the ratio of the area of two triangles.

 

Solution:

 

We know that,

 

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

 

Therefore,

 $ \begin{array}{l}
\frac{ar\vartriangle ABC}{ar\vartriangle DEF} =\left(\frac{AB}{DE}\right)^{2}\\
\\
\frac{ar\vartriangle ABC}{ar\vartriangle DEF} =\left(\frac{19}{8}\right)^{2}\\
\\
\frac{ar\vartriangle ABC}{ar\vartriangle DEF} =\frac{361}{64}
\end{array}$

The ratio of squares of their corresponding sides is $\frac{361}{64}$.