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

• A. y4 = 216 x2
• B. None of these
• C. y2 = 432 x2
• D. y4 = 432 x2

Answer: (D)

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?312?3 x = y2On squaring both sides, we get y4 = 432x2