Question 66

The area of an equilateral triangle is 9√3 sq cm, ﬁnd height of the triangle?

Solution

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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