Question

If the area of an equilateral triangle is 36, find its perimeter. show workin pls

Answer 1

Given :

• Area of an equilateral triangle is 36 units².

To Find :

• Perimeter of the equilateral triangle.

Solution :

Let the length of each side of the equilateral triangle be x units.

We have the formula for calculating the area of the equilateral triangle as follows,

$\large{\boxed{\bold{Area\:=\:\dfrac{\sqrt{3}}{4}\:(side)^2}}}$

Block in the data,

$\sf{\longrightarrow{36\:=\:\dfrac{\sqrt{3}}{4}\:\times\:x^2}}$

$\sf{\longrightarrow{36\:\times\:4\:=\:\sqrt{3}x^2}}$

$\sf{\longrightarrow{144=\sqrt{3}x^2}}$

$\sf{\longrightarrow{\dfrac{144}{\sqrt{3}}=x^2}}$

$\sf{\longrightarrow{\dfrac{144}{1.73}=x^2}}$

$\bold{\big[\because\:\sqrt{3}=1.73\:\big]}$

$\sf{\longrightarrow{83.23=x^2}}$

$\sf{\longrightarrow{\sqrt{83.23}=x^2}}$

$\sf{\longrightarrow{9.12=x}}$

•°• Each side of the equilateral triangle, x = 9.12 units.

Now to calculate the perimeter of the triangle, multiply the length of side by 3.

$\sf{\longrightarrow{Perimeter\:=\:3\:\times\:x}}$

$\sf{\longrightarrow{Perimeter\:=\:3\:\times\:9.12}}$

$\sf{\longrightarrow{Perimeter\:=\:27.36\:units}}$

$\large{\boxed{\bold{Perimter\:of\:equilateral\:triangle\:=\:27.36\:units}}}$

Answer 2

Given :

• Area of an equilateral triangle is 36 units²

To Find :

• Perimeter of the Equilateral Triangle

Solution :

We know that,

$\bigstar \: \boxed{ \sf \: Area_ {Equilateral \: Triangle} = { \dfrac{\sqrt{3}}{4} } \: {side}^{2} }$

$\longrightarrow \sf \: 36 = { \dfrac{\sqrt {3}}{4} } \: {side}^{2}$

$\longrightarrow \sf \: \sqrt{3} \: {side}^{2} = 36 \times 4$

$\longrightarrow \sf \: \sqrt{3} \: {side}^{2} = 144$

$\longrightarrow \sf \: \: {side}^{2} = \dfrac{144}{ \sqrt{3} }$

[√3 = 1.73]

$\longrightarrow \sf \: \: {side}^{2} = \cancel \dfrac{144}{ 1.73}$

$\longrightarrow \sf \: \: {side}^{2} = 83.23$

$\longrightarrow \sf \: \: side = \sqrt{83.23}$

$\longrightarrow \sf \: \: side =9.12 \: units \: \: \: (Approx)$

Now, Let's find Perimeter of the Triangle

$\bigstar \: \boxed{ \sf \: Perimeter_ {Equilateral \: Triangle} = 3 \times side}$

$\longrightarrow \sf \: 3 \times 9.12$

$\longrightarrow \sf \: 27.36 \: units \: \: \: (Approx)$

$\therefore$ Perimeter of the Equilateral Triangle is 27.36 units.