Question

the area of an equilateral triangle is 16√3cm² find the length of it's side is ___​

Answer 1

Answer:

Let the side of triangle be a

The area is given by √3/4a²=16√3

a²=4×16

a²=64

a=√64

a=8cm

Step-by-step explanation:

I hope it is helpful.....

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

Given :

Area of an equilateral triangle is 16√3cm²

To Find:

length of its side

What is an equilateral triangle.??

An equilateral triangle is a triangle which having equal number of sides and each sides having equal angle say 60° each.

$\bold{\boxed{Area \: of \: an \: Equilateral \: Triangle = \frac{ \sqrt{3} }{4} {a}^{2} }}$

Where ,a is side

Now,come to the question:-

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

$= > {a}^{2} = 16 \sqrt{3} \times \frac{4}{ \sqrt{3} }$

$= > {a}^{2} = 16 \times 4 = 64$

$= > {a}^{2} = 64$

$= > a = \sqrt{64} = 8$

$\bold{\red{ = > a = 8cm}}$

Therefore ,the sides of an equilateral triangle are 8cm each.

Check :

$= > \frac{ \sqrt{3} }{4} {8}^{2}$

$= \frac{ \sqrt{3} }{4} \times 64 = 16 \sqrt{3}$