Question

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

Answer 1

Answer:

$AD=\sqrt{3} \ a$

Step-by-step explanation:

AD is perpendicular on BC.

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

Now in the triangle ABD

$AB^{2} =BD^{2} +AD^{2} \ \ \ \ (using \ Pythagorean \ Theorem)\\AD^2=AB^2-BD^2\\AD^2=(2a)^{2} -a^2\\AD^2=3a^2\\AD=a\sqrt{3}$