Question

The ratio of sides of an equilateral triangle to that of a square is `sqrt3 : 1`, then find the ratio of their area.

Options

• `sqrt2 : 3sqrt3`

• 1 : 4

• `sqrt3 : 4`

• None of these

Answer 1

`sqrt3 : 4`

Explanation:

Let side of an equilateral triangle = `sqrt3 "x"`

Area = `sqrt3/4 (sqrt3 "x")^2`

= `sqrt3/4 3"x"^2`

= `(3sqrt3)/4 "x"^2`

Side of a square = x

Area = x²

⇒ Ratio of area = `sqrt3/4 "x"^2 : "x"^2`

= `sqrt3/4 : 1`

= `sqrt3 : 4`