A circle is inscribed in an equilateral triangle of side 24 cm. What is the area (in cm2) of a square inscribed in that circle?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 96
Side of an equilateral triangle = 24 cm
Inradius of equilateral triangle = Side of equilateral triangle/2√3 = 12/√3 cm
Inradius of equilateral triangle = Radius of inscribed circle = 12/√3 cm
Diameter of inscribed circle = Diagonal of inscribed square = 2 × 12/√3 cm = 24/√3 cm
Diagonal of square = √2 × side of square = 24/√3 cm
⇒ Side of square = 24/√6 cm
Hence,
Area of square = (24/√6)2 = 96 cm2