If the area of an equilateral triangle is x and its perimeter

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If the area of an equilateral triangle is x and its perimeter is y, then which one of the following is correct ?

1. y⁴ = 432 x²
2. y⁴ = 216 x²
3. y² = 432 x²
4. None of these

Correct Option: A

Area of equilateral triangle = √3a²/4 = x ......(i)

And perimeter = 3a = y
⇒ a = y/3 ....(ii)

Now, Putting the value of a from Eq. (ii) in Eq. (i). we get
√3 (y/3)²/4 = x
⇒ x = √3 x y²/36
⇒ x = y²/3√3x = y²/12√3
12√3 x = y²
On squaring both sides, we get
y⁴ = 432x²