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

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}}{√(3) }}` .

Explanation:

We are given the area of an Equilateral triangle which is A =
`(√(3) )/(4) * \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 =
`(√(3) )/(4) * \text{s}^(2)`

where, s = side of an equilateral triangle

A =
`(√(3) )/(4) * \text{s}^(2)`

Cross multiplying the fractions we get;

`4 * A = √(3) * \text{s}^(2)`

`√(3) * \text{s}^(2)= 4\text{A}`

Now. moving
`√(3)` to the right side of the equation;

`\text{s}^(2)= \frac{4 \text{A}}{√(3) }`

Taking square root both sides we get;

`\sqrt{\text{s}^(2)} = \sqrt{ \frac{4 \text{A}}{√(3) }}`

`\text{s}= \sqrt{ \frac{4 \text{A}}{√(3) }}`

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