SSC CGL Model Paper 7

Question : 65 of 100

Marks: +1, -0

A circle is inscribed in an equilateral triangle and a square is inscribed in the circle. The ratio of the area of the square to the area of the equilateral triangle is?

${2√3}/3$
$2/√3$
$2/{3√3}$
${2√3}/√7$

Validate

Solution:

Let the side of the ΔABC be 'a' unit
Inradius,

r =a/{2√3}

And area of triangles =

√3/4a^2

→ Then diameter of the circle (PR) =

2×a/2√3=a/√3

→ Since, PR is the diagonals of the square PQRS
Then, side of the square

=a/{√3×√2}=a/√6

Required Ratio

={\Area \of \square}/{\Area \of \equilateral \trianlge}

=(a/√6)^2/{√3/4a^2}=2/{3√3}

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