Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
An equilateral triangle is described on the diagonal of a square. What is the ratio of the area of the triangle to that of the square?
(a)$2: \sqrt{3}$
(b)$4: \sqrt{3}$
(c)$\sqrt{3}: 2$
(d)$\sqrt{3}: 4$
Answer
Answer (as printed): C
Explanation
Let the side of the square be $a \mathrm{cm}$. Then, the length of its diagonal $=\sqrt{2} a \mathrm{cm}$. Area of equilateral triangle with side $$\sqrt{2} a=\frac{\sqrt{3}}{4} \times(\sqrt{2} a)^{2}=\frac{\sqrt{3} a^{2}}{2} \text {. }$$ ∴ Required ratio $=\frac{\sqrt{3} a^{2}}{2}: a^{2}=\sqrt{3}: 2$.