Question

If the area of an equilateral triangle is 16 root 3 find its perimeter

Answer 1

Area of equilateral triangle = (√3a²)/4
16√3 = (√3a²)/4
a² = 64
a = 8cm

Perimeter of equilateral triangle = 3*a = 3*8 = 24cm

Answer 2

Answer:

The perimeter of the equilateral triangle is 24 cm.

Step-by-step explanation:

Given : If the area of an equilateral triangle is $16\sqrt{3}$

To find : Its perimeter ?

Solution :

The area of the equilateral triangle is $A=\frac{\sqrt{3}a^2}{4}$

Here, $A=16\sqrt{3}$

Substitute the value,

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

$a^2=\frac{16\times 4\sqrt{3}}{\sqrt3}$

$a^2=64$

$a=8$

The side of triangle is 8 cm.

The perimeter of the equilateral triangle is $P=3a$

$P=3\times 8$

$P=24\ cm$

Therefore, The perimeter of the equilateral triangle is 24 cm.