Question : A circle is inscribed in an equilateral triangle and a square is inscribed in that circle. The ratio of the areas of the triangle and the square are:
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution :
Given: A circle is inscribed in an equilateral triangle and a square is inscribed in that circle.
Let the sides of the equilateral triangle be
So, area of the equilateral triangle =
The radius of the circle inscribed in the triangle,
Length of the diagonal of the square inscribed in the circle =
Since the diagonal of the square will be the diameter of the circle,
So, the area of the square =
Hence, the correct answer is