Question

Areas of two similar triangles are 72cm² and 162cm², then find the ratio between the lengths of their corresponding sides ​

Answer 1

$\small\bf \colorbox{green}{Verified Answer}$

$\sqrt{ \frac{72}{162} } = \sqrt{ \frac{36}{81} } = \frac{6}{9} = \frac{2}{3} .$

Answer 2

Areas of two similar triangles are 72cm² and 162cm²

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☯ Let these two similar triangles be ∆ ABC and ∆ DEF.

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$\sf Here \begin{cases} & \sf{Area\;of\; \triangle\;ABC = \bf{72\;cm^2}} \\ & \sf{Area\;of\; \triangle\;DEF = \bf{162\;cm^2}} \end{cases}$

We know that,

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• If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

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Therefore,

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$:\implies\sf \dfrac{ar\;(\triangle\;ABC)}{ar\;(\triangle\;DEF)} = \bigg( \dfrac{AB}{BC} \bigg)^2$

$:\implies\sf \cancel{\dfrac{72}{162}} = \bigg( \dfrac{AB}{BC} \bigg)^2$

$:\implies\sf \dfrac{36}{81} = \dfrac{(AB)^2}{(BC)^2}$

$:\implies\sf \dfrac{AB}{BC} = \sqrt{ \dfrac{36}{81}}$

$:\implies\sf \dfrac{AB}{BC} = \cancel{\dfrac{6}{9}}$

$:\implies\sf \dfrac{AB}{BC} = \dfrac{2}{3}$

$:\implies\sf \pink{AB : BC = 2 : 3}$

$\therefore\;{\underline{\sf{Hence,\;Ratio\;of\;length\;of\;their\; corresponding\;sides\;is\; {\bf{\purple{2:3}}}.}}}$