Practicing Success
The perimeter of an equilateral triangle is equal to circumference of a circle. The ratio of their areas is: |
22 : 21\(\sqrt {3}\) 21\(\sqrt {3}\) : 63 21 : 22\(\sqrt {3}\) 21\(\sqrt {3}\) : 22 |
22 : 21\(\sqrt {3}\) |
Perimeter of equilateral triangle = 3a ATQ, ⇒ 3a = circumference of circle ⇒ 3a = 2\(\pi\)r ⇒ a : r = 2\(\pi\) : 3 Area of circle = \(\pi r^2\) Area of equilateral triangle = \(\frac{\sqrt {3}}{4} a^2\) Required ratio = \(\frac{\sqrt {3}}{4} a^2\) : \(\pi r^2\) = \(\frac{\sqrt {3}}{4}\) (2\(\pi\))2 : \(\pi\) 32 = \(\pi\) : 3\(\sqrt {3}\) = 22 : 21\(\sqrt {3}\) |