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Question
Find the height of an equilateral triangle having side 2a.
Solution
Since, ABC is an equilateral triangle, AD is the perpendicular bisector of BC.
According to Pythagoras theorem,
In ∆ABD,
AB2 = AD2 + BD2
∴ (2a)2 = AD2 + a2
∴ 4a2 − a2 = AD2
∴ AD2 = 3a2
∴ AD = `sqrt3`a
Hence, the height of an equilateral triangle is `sqrt3`a
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