Question

the perimeter of an equilateral triangle is √3 times its area. find the length of each side?? please please friend show step by step?? please please it's urgent?

Answer 1

We know that perimeter of an equilateral triangle = 3a.

Also,

We know that Area of equilateral triangle = $\frac{\sqrt{3}}{4} a^2$

According to the question,

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

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

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

= > a = 4.

Therefore, the length of each side = 4units

Hope this helps!

Answer 2

Heya!!

Perimeter of an equilateral triangle = 3*side,
Area of an equilateral triangle = √3/ 4 * (side) ^2

Let the side of an equilateral triangle be x.

According to question,

=) 3x = √3* √3/ 4 * x^2

=) 3x = 3/4 * x^2

=) 3x * 4 / 3x = x

=) 4 = x

Hence side of an equilateral triangle is 4 units.

Hope it helps uh :)