Maharashtra State Board course SSC (English Medium) Class 10th Board Exam
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Solve the Following Example. Find the Height of an Equilateral Triangle Having Side 2a. - Geometry

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Question

Solve the following example.

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

Solution


Since, ABC is an equilateral triangle, AD is the perpendicular bisector of BC.
Now, According to Pythagoras theorem,
In ∆ABD

\[{AB}^2 = {AD}^2 + {BD}^2 \]
\[ \Rightarrow \left( 2a \right)^2 = {AD}^2 + a^2 \]
\[ \Rightarrow 4 a^2 - a^2 = {AD}^2 \]
\[ \Rightarrow {AD}^2 = 3 a^2 \]
\[ \Rightarrow AD = \sqrt{3}a\]

Hence, the height of an equilateral triangle is

\[\sqrt{3}a\]
  Is there an error in this question or solution?

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Solution Solve the Following Example. Find the Height of an Equilateral Triangle Having Side 2a. Concept: Apollonius Theorem.
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