The perimeter of a square and a regular hexagon are equal. The ratio of the area of the hexagon to the area of the square is:
Options:
$2\sqrt{3}:1$
$2:\sqrt{3}$
$3\sqrt{3}:2$
$\sqrt{2}:3$
Correct Answer:
$2:\sqrt{3}$
Explanation:
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
Thus, a=3b/2 Area of the square =a2 Area of the hexagon =(3√3)b2/2 Now, Area of hexagon : Area of square =(3√3)b2/2 : a2 ⇒(3√3)b2/2 : (3b/2)2 ⇒ (3√3)b2/2 : 9b2/4 ⇒ 3√3/2 : 9/4 ⇒ 2 : √3
