Solve the following example. Find the height of an equilateral triangle having side 2a. - Geometry Mathematics 2

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Sum

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

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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Chapter 2: Pythagoras Theorem - Problem Set 2 [Page 44]

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