Question

area of an equilateral triangle is root 3 by 2 cm square then find the side of a triangle​

Answer 1

Answer:

$\red {Side \: of \:the \: triangle }\green {=\sqrt{2}\:cm}$

Step-by-step explanation:

$Let \: the \:side \: of \: an \: equilateral\: triangle = a \: cm$

$\boxed { \pink { Area \: of \: equilateral \: triangle (A)= \frac{\sqrt{3}}{4}\: a^{2}}}$

$A = \frac{\sqrt{3}}{2} \:(given)$

$\implies \frac{\sqrt{3}}{4}\: a^{2} = \frac{\sqrt{3}}{2}$

$\implies a^{2} = \frac{\sqrt{3}}{2} \times \frac{4}{\sqrt{3}}$

$= 2$

$\implies a = \sqrt{2}\:cm$

Therefore.,

$\red {Side \: of \:the \: triangle }\green {=\sqrt{2}\:cm}$

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Answer 2

$\purple{ \mathtt{ \huge \underline{ \fbox{ \: Solution : \: \: }}}}$

Given ,

Area of equilateral triangle = √3/2 cm²

We know that , the area of equilateral triangle is given by

$\star \: \large \mathtt{ \fbox{Area \: of \: equilateral \: \triangle = \frac{ \sqrt{3} }{4} \times {(a)}^{2} }}$

Substitute the values , we obtain

$\sf \hookrightarrow \frac{ \sqrt{3} }{2} = \frac{ \sqrt{3} }{4} \times {(a)}^{2} \\ \\ \sf \hookrightarrow {(a)}^{2} =\frac{ \cancel{ \sqrt{3}} }{ \cancel2} \times \frac{ \cancel 4 }{ \cancel{ \sqrt{3}} } \\ \\ \sf \hookrightarrow {(a)}^{2} = 2 \\ \\ \sf \hookrightarrow a = \sqrt{2} \: \: cm$

Hence , the side of equilateral triangle is √2 cm