Question

Question text The areas of two similar triangles ABC and PQR are 25 cm2 and 49 cm2 respectively. If QR = 9.8 cm, find BC
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Answer 1

this could be the possible answer

Answer 2

$Area \: of \: \triangle ABC = 25 \:cm^{2} \\ \: Area \: of \: \triangle PQR = 49 \:cm^{2} \\and \: QR = 9.8 \:cm , \: \red{BC = ? }$

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$\blue {( The \:ratio \:of \:the \: areas\: of \:two}\\\blue{similar \: triangles \: is \: equal \: to \:the}\\\blue{ ratio \: of \: the \: squares \:of \:their}\\\blue{ corresponding \:sides)}$

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$\Big( \frac{BC}{QR}\Big)^{2} = \frac{ ar(\triangle ABC)}{ar(\triangle PQR )}$

$\implies \Big( \frac{BC}{9.8}\Big)^{2} =\frac{25}{49}$

$\implies \Big( \frac{BC}{9.8}\Big)^{2} =\frac{5^{2}}{7^{2}}$

$\implies \Big( \frac{BC}{9.8}\Big)^{2} =\Big(\frac{5}{7}\Big)^{2}$

$\implies \frac{BC}{9.8} = \frac{5}{7}$

$\implies BC = \frac{5}{7}\times 9.8$

$\implies BC = 5 \times 1.4$

$\implies BC = 7 \:cm$

Therefore.,

$\red{ Value \:of \: BC } \green {= 7 \:cm }$

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