Question

If the area of an equilateral triangle is 9√3 2

, then its perimeter is​

Answer 1

Given:

• Area of an Equilateral Triangle = 9√3 cm²

To find:

⟶ Perimeter = ?

Concepts used:

1. Area of an Equilateral Triangle =

Method:

Let 'a' be the side of an equilateral triangle.

$\sf{Area\: of \: an \: Equilateral \: Triangle = \dfrac{\sqrt{3} a^{2} }{4}}\\\\\\\implies \sf{9\sqrt{3} = \dfrac{\sqrt{3} a^{2} }{4}}\\\\\\\\\implies \sf{9\sqrt{3} \times 4 = \sqrt{3} a^{2} }\\\\\\\implies \sf{\dfrac{36 \sqrt{3}}{\sqrt{3} } = a^{2} }\\\\\\\implies \sf{a^{2} = 36}\\\\\\\implies \sf{a=\pm6}\\\\\\\tt{Side\:cannot\:be\:negative}\\\\\\\therefore \large \boxed{\bf{a = 6 \: units}}$

$\sf{Perimeter=3\times side}\\\\\implies \sf{Perimeter=3a}\\\\\implies \sf{Perimeter=3 \times 6}\\\\\\\implies \large{\boxed{\bf{Perimeter = 18\:units}}}$