Question

The area of an Equilateral triangle is given by the formula A= 3pi squared/4(s)Squared. Which formula represents the length of equilateral triangle’s side S?

Answer 1

Answer:

The formula that represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A) is $\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}$ .

Step-by-step explanation:

We are given the area of an Equilateral triangle which is A = $\frac{\sqrt{3} }{4} \times \text{s}^{2}$ . And we have to represent the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).

So, the area of an equilateral triangle =  $\frac{\sqrt{3} }{4} \times \text{s}^{2}$

where, s = side of an equilateral triangle

A  =  $\frac{\sqrt{3} }{4} \times \text{s}^{2}$

Cross multiplying the fractions we get;

$4 \times A = \sqrt{3} \times \text{s}^{2}$

$\sqrt{3} \times \text{s}^{2}= 4\text{A}$

Now. moving $\sqrt{3}$ to the right side of the equation;

$\text{s}^{2}= \frac{4 \text{A}}{\sqrt{3} }$

Taking square root both sides we get;

$\sqrt{\text{s}^{2}} = \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}$

$\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}$

Hence, this formula represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).