Question

if the area of eqilateral triangle is 16√3 cm^2, then its perimeter of triangle is ​

Answer 1

Answer:

$\huge \mathcal{ \fcolorbox{aqua}{azure}{ \green{ANSWER}}}$

Given, area of an equilateral triangle = 16√3 cm2

Area of an equilateral triangle = √3/4 (side)2

√3/4(Side)2 = 16√3 ⇒ (Side)2 = 64

⇒ Side =8 cm

[taking positive square root because side is always positive]

Perimeter of an equilateral triangle = 3 x Side= 3 x 8 = 24 cm

Hence, the perimeter of an equilateral triangle is 24 cm.

Answer 2

Answer:

The answer to this question is 24cm

Step-by-step explanation:

We know An equilateral triangle is a triangle whose all three sides are having the same length.

The area of an equilateral triangle with side $a$ is $\frac{\sqrt{3}}{4}a^2$

Now given that the area of the equilateral triangle is $16\sqrt{3} \text{ cm}^2$

$\frac{\sqrt{3}a^2}{4} = 16\sqrt{3}\\or, \frac{a^2}{4} = 16\\or, a^2 = 64\\or, a= 8$

(NOTE: Here $a$ cannot be -8 because side length can never be less than 0)

Therefore,the Perimeter of the triangle is $3a = 24cm$