Triangles ABC and DEF are similar.If $AB\ =\ 1.2\ cm$ and $DE\ =\ 1.4\ cm$, find the ratio of the area of two triangles.
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Given:

 

Triangles ABC and DEF are similar.

 

$AB\ =\ 1.2\ cm$ and $DE\ =\ 1.4\ cm$.

 

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{1.2}{1.4}\right)^{2}\\
\\
\frac{ar\vartriangle ABC}{ar\vartriangle DEF} =\left(\frac{12}{14}\right)^{2}\\
\\
\frac{ar\vartriangle ABC}{ar\vartriangle DEF} =\left(\frac{6}{7}\right)^{2}\\
\\
\frac{ar\vartriangle ABC}{ar\vartriangle DEF} =\frac{36}{49}
\end{array}$

The ratio of the area of two triangles is $36:49$.