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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

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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