Question

the area of two similar triangles are 32 cm 2 and 48cm 2. If square of a side of the first triangle is 24 cm 2, then the corresponding sides of 2nd triangle will be what?

Answer 1

Here is your answer friend.

Answer 2

$Let \: \triangle ABC \sim \triangle DEF$

$ar( \triangle ABC) = 32 \:cm^{2} \: and \\ar( \triangle DEF) = 48 \:cm^{2}$

$AB^{2} = 24 \:cm^{2} ,\: \red { DE = ? }$

/* We know that,

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

$\Big( \frac{ ar( \triangle ABC)}{ar( \triangle DEF)} \Big) = \Big( \frac{AB^{2}}{DE^{2}}\Big)$

$\implies \frac{ 32}{48} = \frac{24}{DE^{2}}$

$\implies DE^{2} = \frac{24 \times 48}{32}$

$\implies DE^{2} = 36$

$\implies DE = \sqrt{6^{2}}$

$\implies DE =6\: cm$

Therefore.,

$\red { Corresponding \:side \: second \triangle} \\\green {= 6\: cm}$

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