The area of an equilateral triangle is 9√3 sq cm, find height of the triangle?
Let the side of equilateral triangle = $$a$$ cm
Area of equilateral triangle = $$\frac{\sqrt{3}}{4} a^2 = 9 \sqrt{3}$$
=> $$a^2 = 9 \times 4 = 36$$
=> $$a = \sqrt{36} = 6$$ cm
The height $$h$$ of an equilateral triangle bisect the opposite side.
=> $$(h)^2 = (6)^2 - (3)^2$$
=> $$(h)^2 = 36 - 9 = 27$$
=> $$h = \sqrt{27} = 3\sqrt{3}$$ cm
=> Ans - (C)
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