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Solve the following example.

Find the height of an equilateral triangle having side 2a.

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#### Solution

Since, ABC is an equilateral triangle, AD is the perpendicular bisector of BC.

Now, According to Pythagoras theorem,

In ∆ABD

AB^{2} = AD^{2} + BD^{2}

⇒ (2a)^{2} = AD^{2} + a^{2}

⇒ 4a^{2} - a^{2} = AD^{2}

⇒ AD^{2} = 3a^{2}

⇒ AD = `sqrt3`a

Hence, the height of an equilateral triangle is `sqrt3`a

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