The side of a square is equal to the side of an equilateral triangle.
Question:

The side of a square is equal to the side of an equilateral triangle. The ratio of their areas is
(a) 4 : 3

(b) $2: \sqrt{3}$

(c) $4: \sqrt{3}$

(d) none of these

Solution:

(c) $4: \sqrt{3}$

Let:
Length of the side of the square = Length of the side of the equilateral triangle = a unit

Now,

Area of the square $=a \times a=a^{2}$ unit $^{2}$

Area of the equilateral triangle $=\frac{\sqrt{3}}{4} a^{2} \mathrm{unit}^{2}$

Ratio of areas $=\frac{\text { Area of the square }}{\text { Area of the equilateral triangle }}$

$=\frac{a^{2}}{\frac{\sqrt{3}}{4} a^{2}}$

$=\frac{4}{\sqrt{3}}$