Correct : b

Formulas for Area and Perimeter:
•     Equilateral Triangle with side length s:
    Area (A_t) = (s²√3) / 4
    Perimeter (P_t) = 3s
•     Square with side length a:
    Area (A_s) = a²
    Perimeter (P_s) = 4a
•     Circle with radius r:
    Area (A_c) = πr²
    Perimeter (P_c) = 2πr
Express Side/Radius in terms of Area (A):
Since A_t = A_s = A_c = A:
•     For the equilateral triangle:
    A = (s²√3) / 4
    s² = 4A / √3
    s = √(4A / √3) = 2√A / (3^1/4)
•     For the square:
    A = a²
    a = √A
•     For the circle:
    A = πr²
    r² = A / π
    r = √(A / π) = √A / √π
Calculate Perimeters in terms of Area (A):
•     For the equilateral triangle (P_t):
    P_t = 3s = 3 × (2√A / 3^1/4) = 6√A / 3^1/4
    To simplify 6 / 3^1/4:
    6 / 3^1/4 = (2 × 3) / 3^1/4 = 2 × 3^{1 - 1/4} = 2 × 3^3/4
    Note that 3^3/4 = (3³)^1/4 = 27^1/4 = √√27.     Also, √(3√3) = (3 × 3^1/2)^1/2 = (3^3/2)^1/2 = 3^3/4.
    So, P_t = 2√A × √(3√3)
•     For the square (P_s):
    P_s = 4a = 4√A
•     For the circle (P_c):
    P_c = 2πr = 2π × (√A / √π) = 2√A√π
Determine the Ratio of Perimeters:
P_t : P_s : P_c = (2√A × √(3√3)) : (4√A) : (2√A√π)
Divide all terms by 2√A (since A is a positive area, √A ≠ 0):
√(3√3) : 2 : √π