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 $\frac{361}{64}$.
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