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ABC is an equilateral triangle of side 2a. Find each of its altitudes.

Q6   ABC is an equilateral triangle of side 2a. Find each of its altitudes.

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Given: ABC is an equilateral triangle of side 2a.

AB=BC=AC=2a

AD is perpendicular on BC.

We know that altitude of an equilateral triangle bisects opposite side.

  So, BD=CD=a

In \triangle ADB,

By Pythagoras theorem,

AB^2=AD^2+BD^2

\Rightarrow (2a)^2=AD^2+a^2

\Rightarrow 4a^2=AD^2+a^2

\Rightarrow 4a^2-a^2=AD^2

\Rightarrow 3a^2=AD^2

\Rightarrow AD=\sqrt{3}a

Length of each altitude is \sqrt{3}a.

 

 

 

 

 

 

 

 

 

 

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