Triangles ABC and DEF are similar.
If area of $(ΔABC)\ =\ 36\ cm^2$, area $(ΔDEF)\ =\ 64\ cm^2$ and $DE\ =\ 6.2\ cm$, find $AB$.

"

Given:

 

Triangles ABC and DEF are similar.

 

Area of $(ΔABC)\ =\ 36\ cm^2$, area $(ΔDEF)\ =\ 64\ cm^2$ and $DE\ =\ 6.2\ cm$.

 

To do:

 

We have to find $AB$.

 

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{36}{64} =\left(\frac{AB}{6.2}\right)^{2}\\
\\
\frac{AB}{6.2} =\sqrt{\frac{36}{64}}\\
\\
AB=\frac{6.2\times 6}{8}\\
\\
AB=\frac{37.2}{8}\\
\\
AB=4.65\ cm
\end{array}$

The value of $AB$ is $4.65\ cm$.