Question

If the area of an equilateral triangle is under root 3/4cm^2 then find the length of its each side

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Sides=\sqrt{2}\:cm}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Area \: of \: equilateral \: triangle = \frac{3}{4} { \: cm}^{2} \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Length \: of \: each \: side =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: equilateral \: triangle = \sqrt{ \frac{3}{4} } \: {cm}^{2} \\ \\ \tt: \implies \frac{ \sqrt{3} }{4} {side}^{2} = \sqrt{ \frac{3}{4} } \\ \\ \tt: \implies {side}^{2} = \frac{ \sqrt{3} }{2} \times \frac{4}{ \sqrt{3} } \\ \\ \tt: \implies {side}^{2} = 2 \\ \\ \green{\tt: \implies side = \sqrt{2} \: cm} \\ \\ \green{\tt \therefore Sides \: of \: triangle = \sqrt{2} \: cm \: each}\\\\ \blue{\bold{Some\:related\:formula}}\\\\ \orange{\tt\circ\:Area\:of\:triangle=\frac{1}{2}\times b\times h}\\\\ \orange{\tt\circ\:Area\:of\:triangle=\sqrt{s(s-a)(s-b)(s-c)}}$

Answer 2

ANSWER:

Given

• Area of equilateral triangle = √3/4 cm²

We know that

Area of equilateral triangle = √3/4 (side)²

$\tt{ \to \dfrac{ \sqrt{3} }{4} \times {s}^{2} = \sqrt{ \dfrac{3}{4} } } \\ \\ \tt{\to {s}^{2} = \sqrt{\frac{3}{4}} \times \frac{4}{ \sqrt{3} } } \\ \\ \to{ \tt{ {s}^{2} } = \frac{ \cancel{\sqrt{3}} } { \cancel2} \times \frac{ \cancel4}{ \cancel{\sqrt{3}} } } \\ \\ \to \tt{ {side} = \sqrt{2} }$

We know that

Equilateral triangle : A triangle which has three equal sides

Hence, length of each side = √2