Question

Two vertices of an equilateral triangle lie on a diameter of a circle whose area is 36p cm2, and the third vertex lies on the circle. What is the largest possible area of the triangle?

Answer 1

The maximum area of the equilateral triangle willl be possible when the height of the equilateral triangle = radius of the circle.

For an equilateral triangle, the height is given as , where a is the side of the equilateral triangle.

Given that the area of the circle = = 36 *

Therefore r² = 36 or r = 6

Therefore we have = 6

Solving for a, we get a =

Area of an Equilateral Triangle is given as

Therefore Area =

Maximum Area = = 20.7846 cm².