Question

If The Area Of Equilateral Triangle Is 36Square Root 3 Cm Sq. What Is The Perimeter Of This Triangle

Answer 1

Answer:-

p = 36 cm

Given :-

Area of equilateral triangle = 36 √3 cm²

To find :-

Perimeter of equilateral triangle.

Solution :-

First we have to find the side of equilateral triangle.

Area of equilateral triangle is given by :-

★ $\boxed{\sf{A = \dfrac{\sqrt{3}}{4}\times (Side) ^2}}$

Now, put the given value,

→$36\sqrt{3} = \dfrac{\sqrt{3}}{4}\times (Side)^2$

→$36\sqrt{3}\times 4 = \sqrt{3}\times (Side)^2$

→$144\sqrt{3}=\sqrt{3}(Side) ^2$

→$(Side)^2 = \dfrac{144\sqrt{3}}{\sqrt{3}}$

→$(Side) ^2 = 144$

→$Side = \sqrt{144}$

→$Side = 12 cm$

Now perimeter of an equilateral triangle = 3 × side

= 3 × 12

= 36 cm

hence, perimeter of given equilateral triangle will be = 36 cm

Answer 2

Answer:

Perimeter = 36 cm.

Step-by-step explanation:

Given Problem:

If The Area Of Equilateral Triangle Is 36Square Root 3 Cm Sq. What Is The Perimeter Of This Triangle.

Solution:

The first step is to find the side of equilateral triangle.

★We know that, ★

★$A = \dfrac{\sqrt{3} }{4}\times(Side)^2$ ★

Now Plug the values in equation,

$\implies\ 36\sqrt{3} \times 4 = \sqrt{3} \times(Side)^2$

$\implies\ 144\sqrt{3} = \sqrt{3}(Side)^2$

$\implies\ (Side)^2 = \dfrac{144\sqrt{3} }{\sqrt{3} }$

$\implies\ (Side)^2 = 144$

$\implies\ Side = \sqrt{144}$

$So,\\Side = 12cm$

Now,

We know that,

★Perimeter = (Side + Side + Side)★

= > (12 + 12 + 12) cm = 36 cm

= > 36 cm

Hence,

It implies that the perimeter of given equilateral triangle is  36 cm.