Question

An equilateral triangle is drawn on the diagonal of a square. The ratio of the area of the triangle to that of the square is

• A. $$\sqrt{3}:2$$
• B. $$\sqrt{2}:\sqrt{3}$$
• C. $$2:\sqrt{3}$$
• D. $$1:\sqrt{2}$$

Answer 1

Answer:

$$\sqrt{3}:2$$

Let the side of the square be x units,

then diagonal $= \sqrt{2}x units$

Area of the square $=x^2$

and area of triangle $=\frac{\sqrt{3}}{4}(\sqrt{2}x)^2$

$=\frac{\sqrt{3}x^2}{2}$ sq.units

Required Ratio $=\frac{\sqrt{3}x^2}{2}:x^2$

=>\sqrt{3}:2