• If the area of an equilateral triangle is x and its perimeter is y. then which one of the following is correct?
 A) $$\Large y^{4}=432x^{2}$$ B) $$\Large y^{4}=216x^{2}$$ C) $$\Large y^{2}=432x^{2}$$ D) None of these

 A) $$\Large y^{4}=432x^{2}$$

Area of equilateral triangle

$$\Large \frac{\sqrt{3} a^{2}}{4}$$=x ....(i)

and perimeter = 3a = y => a = $$\Large \frac{y}{3}$$ ...(ii)

Now, putting the value of a from Eq. (ii) in Eq. (i), we get

$$\Large \frac{\sqrt{3}\left(\frac{y}{3}\right)^{2}}{4}$$=x => x=$$\Large \frac{\sqrt{3}\times y^{2}}{9\times 4}$$

=> x=$$\Large \frac{y^{2}}{3\sqrt{3}\times 4}$$ => x=$$\Large \frac{y^{2}}{12\sqrt{3}}$$

=> $$\Large 12\sqrt{3}x=y^{2}$$

On squaring both sides, we get

$$\Large y^{4}=432x^{2}$$

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