Question

the perimeter of an equilateral triangle is root 3 times its area . find the lenght
of each side​

Answer 1

Answer:

Correct Answer is 4

Step-by-step explanation:

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Answer 2

Given :-

The perimeter of an equilateral triangle is √3 times its area.

To Find :-

The length of each side.

Solution :-

We know that,

• p = Perimeter
• a = Side

By the formula,

Perimeter of an equilateral triangle = 3a

$\underline{\boxed{\sf Area \ of \ equilateral \ triangle=\dfrac{\sqrt{3} }{4} a^{2}}}$

Given that,

The perimeter of an equilateral triangle is √3 times its area.

According to the question,

$\sf 3a=\sqrt{3} \times \dfrac{\sqrt{3} }{4} a^{2}$

$\sf 3a=\dfrac{\sqrt{3} \times \sqrt{3} }{4} a^{2}$

$\sf 3a=\dfrac{3}{4} a^{2}$

$\sf a=\dfrac{3a \times 4}{3a}$

$\sf a=4$

Therefore, each side of the equilateral triangle is 4 units.