Question

the triangle ABC and DEF are similar. if their area are 100cm2 and 49cm2 respectively and BC is 8.2 CM then EF​

Answer 1

Answer:

5.74cm

Step-by-step explanation:

Answer 2

$Given \: \triangle ABC \sim \triangle DEF$

$Area \: of \: \triangle ABC = 100 \:cm^{2} \\ Area \: of \: \triangle DEF = 49 \:cm^{2} \\and \: BC = 8.2 \:cm$

$\underline{ \red{ To \: find : }}$

$EF = ?$

/* We know that */

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

$\frac{Area \: of \:\triangle ABC}{Area \: of \:\triangle DEF } = \frac{BC^{2}}{EF^{2}}$

$\implies \frac{100}{49} = \Big(\frac{BC}{EF}\Big)^{2}$

$\implies \Big(\frac{10}{7}\Big)^{2} = \Big(\frac{8.2}{EF}\Big)^{2}$

$\implies \frac{10}{7} = \frac{8.2}{EF}$

$\implies EF = 8.2 \times \frac{7}{10}$

$\implies EF = 5.74$

Therefore.,

$\red{ Value \: of \: EF } \green { = 5.74 \:cm }$

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