Question

the area of an equilateral triangle is 16 under root 3 cm square find its perimeter​

Answer 1

Hello Dear friend

Given, area of an equilateral triangle is

$\large{16 \sqrt{3} }$

We know that area of equilateral triangle=

$\large{ \frac{ \large{ \sqrt{3} }}{ \: \: \: \large{4}} \: {a}^{2} }$

ATQ,

$\large{ \frac{ \large{ \sqrt{3} }}{ \: \: \: \large{4}} \: {a}^{2} = 16 \sqrt{ 3} }$

$\large{ \frac{ \: \large{ {a}^{2} }}{ \: \large{4}} = 16}$

$\large{ {a}^{2} = 64 }$

$\large{a = \sqrt{64} }$

$\large{ \boxed{a = 8 \: cm}}$

so, length of its side =

$\large{ {a = \underline{8 \: cm}}}$

perimeter = 3a

= 3 × 8

$\large \boxed{.`. \: \: perimeter = \: \boxed{ 24 \: cm}}$

HOPE IT HELPS