Question

A square and a regular hexagon have equal perimeters. Their areas are in the ratio: 

(a) 2 : 1

(b) 2√3 :1

(c) √3 : 2

(d) 3 : 2

Answer 1

Correct option is (c) √3 : 2

Let the side of the square = a.

Perimeter of the square = 4a

Let the side of the hexagon = b

Perimeter of the hexagon = 6b

Given, 4a = 6b

⇒ a = \(\frac 32 b\)

Area of the square = a²

Area of the hexagon = \(\frac {3\sqrt3}2 b^2\)

Now, Area of square : Area of hexagon = a² : \(\frac {3\sqrt3}2 b^2\)