Triangles ABC and DEF are similar.
If area $(ΔABC)\ =\ 9\ cm^2$, area $(ΔDEF)\ =\ 64\ cm^2$ and $DE\ =\ 5.1\ cm$, find $AB$.

"

Given:

Triangles ABC and DEF are similar.

Area $(ΔABC)\ =\ 9\ cm^2$, area $(ΔDEF)\ =\ 64\ cm^2$ and $DE\ =\ 5.1\ cm$.

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{9}{64} =\left(\frac{AB}{5.1}\right)^{2}\\
\\
\frac{AB}{5.1} =\sqrt{\frac{9}{64}}\\
\\
AB=\frac{5.1\times 3}{8}\\
\\
AB=\frac{15.3}{8}\\
\\
AB=1.9125\ cm
\end{array}$

The value of $AB$ is $1.9125\ cm$.

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Updated on: 10-Oct-2022

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