A) \[{{y}^{4}}=~432{{x}^{2}}\]
B) \[{{y}^{4}}=~216{{x}^{2}}\]
C) \[{{y}^{2}}=~432{{x}^{2}}\]
D) None of the above
Correct Answer: A
Solution :
Area of equilateral triangle = \[\frac{\sqrt{3}{{a}^{2}}}{1}=x\] ? (1) and perimeter = 3a = y \[\Rightarrow \] a= \[\frac{y}{3}\] ...(ii) Now, putting the value of a from Eq. (ii) in Eq. (i), we get, \[\frac{\sqrt{3}{{\left( \frac{y}{3} \right)}^{2}}}{4}=x\] \[\Rightarrow \,\,\,\,\,\,\,x=\frac{{{y}^{2}}}{12\sqrt{3}}\Rightarrow 12\sqrt{3}x={{y}^{2}}\] On squaring both sides, we get y4 = 432x2
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