CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

The question is from CAT Geometry - Triangles. In this problem it discusses about the relation between the sides of square , triangle and the radius of the circle. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems.

Question 22: A circle inscribed in a square of side 2 has an equilateral triangle inscribed inside it. What is the ratio of areas of the equilateral triangle to that of the square?

1. 9√3 : 16
2. 3√3 : 4
3. 9√3 : 4
4. 3√3 : 16

Explanatory Answer

Method of solving this CAT Question from Triangles: If you find the relation between the sides of square , triangle and the radius , then you are through!!

The radius of the circle is 1 unit.
If we considered the side of the equilateral triangle to be ‘a’, the circumradius of an equilateral triangle is R = \\frac{a}{√3}\\)
Therefore, a = √3
So, ratio of areas of the equilateral triangle to that of the square is

\\frac{√3}{4}\\) * (√3)² : 2²
3 \\frac{√3}{4}\\) : 4
3√3 : 16

The question is "What is the ratio of areas of the equilateral triangle to that of the square? "

Hence, the answer is 3√3 : 16 Units

Choice D is the correct answer.