Question

What is the perimeter of a triangle if area of an equilateral triangle is 9 under root 3

Answer 1

Answer:

$\sf{The \ perimeter \ of \ the \ equilateral \ triangle \ is}$

$\sf{18 \ units.}$

Given:

• $\sf{For \ equilateral \ triangle, }$
• $\sf{\leadsto{Area=9\sqrt3 \ unit^{2}}}$

To find:

• $\sf{The \ perimeter \ of \ the \ eqilateral \ triangle.}$

Solution:

$\boxed{\sf{Area \ of \ equilateral \ triangle=\dfrac{\sqrt3}{4}\times \ Side^{2}}}$

$\sf{\therefore{9\sqrt3=\dfrac{sqrt3}{4}\times \ Side^{2}}}$

$\sf{\therefore{Side^{2}=9\sqrt3\times\dfrac{4}{\sqrt3}}}$

$\sf{\therefore{Side^{2}=36}}$

$\sf{On \ taking \ square \ root \ of \ both \ sides}$

$\sf{\longmapsto{Side=6 \ units}}$

$\boxed{\sf{Perimeter \ of \ equilateral \ triangle=3\times \ Side}}$

$\sf{\therefore{Perimeter \ of \ equilateral \ triange=3\times6}}$

$\sf{\therefore{Perimeter \ of \ equilateral \ triange=18 \ units}}$

$\sf\purple{\tt{\therefore{The \ perimeter \ of \ the \ equilateral \ triangle \ is}}}$

$\sf\purple{\tt{18 \ units.}}$