Triangles ABC and DEF are similar.
If area of $(ΔABC)\ =\ 16\ cm^2$, area $(ΔDEF)\ =\ 25\ cm^2$ and $BC\ =\ 2.3\ cm$, find $EF$.

"

Given:

Triangles ABC and DEF are similar.

Area of $(ΔABC)\ =\ 16\ cm^2$, area $(ΔDEF)\ =\ 25\ cm^2$ and $BC\ =\ 2.3\ cm$.

To do:

We have to find $EF$.

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{BC}{EF}\right)^{2}\\
\\
\frac{16}{25} =\left(\frac{2.3}{EF}\right)^{2}\\
\\
\frac{EF}{2.3} =\sqrt{\frac{25}{16}}\\
\\
EF=\frac{5\times 2.3}{4}\\
\\
EF=\frac{11.5}{4}\\
\\
EF=2.875\ cm
\end{array}$

The value of $EF$ is $2.875\ cm$.

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Updated on: 10-Oct-2022

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