Question

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

Answer 1

`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)`