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In an equilateral triangle ABC of side 2a,AD perpendicular to BC,then find the length of AD.

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Answer:


AD=√(3) \ a

Explanation:

AD is perpendicular on BC.

BD=CD=a (as D is the mid point of BC)

Now in the triangle ABD


AB^(2) =BD^(2) +AD^(2) \ \ \ \ (using \ Pythagorean \ Theorem)\\AD^2=AB^2-BD^2\\AD^2=(2a)^(2) -a^2\\AD^2=3a^2\\AD=a√(3)

In an equilateral triangle ABC of side 2a,AD perpendicular to BC,then find the length-example-1
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