Question

If area of an equilateral triangle is 81 root 3 cm sq .find its perimeter

Answer 1

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Answer 2

$\huge{\bf{\underline{\red{Solution :}}}}$

Suppose the side of Equilateral triangle be a cm

We know ,

Area of Equilateral triangle = $\bold{\frac{\sqrt{3} a }4} \ \bold{cm^{2}}$

Now According to Question :

$\implies \bold{\frac{\sqrt{3} }{4} a^{2} } = \bold{ 81\sqrt{3}}$

$\implies \bold{a^{2} = 81 \times 4 }$

$\implies \bold{ a = \sqrt{81 \times 4 } }$

$\implies \bold{a = 9 \times 2 }$

$\implies \bold{18 \ cm}$

∴Now Perimeter of Equilateral Triangle :

We know that perimeter of Equilateral triangle = 3a

⇒3 x 18

⇒54 cm (Answer)

$\rule{200}2$

Area of Equilateral Triangle :

⇒If the side of equilateral triangle is a so its semi- perimeter :

$\implies \bold{ s = \frac{a + a + a }{2} }$

$\implies \bold{\frac{3a}{2}}$

Now Heron's Formula to find Area of equilateral triangle :

$\implies \bold{\sqrt{\frac{3a}{2}[\frac{3a}{2} - a ] [ \frac{3a}{2} - a ] [ \frac{3a}{2} - a] } }$

$\implies \bold{\sqrt{\frac{3a}{2} \times \frac{a}{2} \times \frac{a}{2} \times \frac{a}{2}} }$

$\implies \huge{\bf{\star{\frac{\sqrt{3} a^{2} }{4} unit^{2} }}}$