Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
A circle is inscribed in a square. An equilateral triangle of side $4 \sqrt{3} \mathrm{cm}$ is inscribed in that circle. The length of the diagonal of the square is
(a)$4 \sqrt{2} \mathrm{cm}$
(b)8 cm
(c)$8 \sqrt{2} \mathrm{cm}$
(d)16 cm
Answer
Answer (as printed): C
Explanation
Side of equilateral triangle, $a=4 \sqrt{3} \mathrm{cm}$. Radius of circle, $$r=\frac{a}{\sqrt{3}}=\left(\frac{4 \sqrt{3}}{\sqrt{3}}\right) \mathrm{cm}=4 \mathrm{cm} .$$ Let each side of the square be $x \mathrm{cm}$. Then, $x=2 r=8 \mathrm{cm}$. ∴ Diagonal of the square $$=\sqrt{8^{2}+8^{2}} \mathrm{cm}=\sqrt{128} \mathrm{cm}=8 \sqrt{2} \mathrm{cm} .$$