Question

In an equilateral triangle ABC,D is paint on side BC Such that BD= ⅓ prove that a (AD^2)= 7 (AB)^2

Answer 1

Draw a perpendicular from AP on BC .

Let side of equilateral triangle be a,
Then find height of perpendicular
Using Pythagoras theroram in triangle ADP
we get, AD²=AP²+PA²
( PUT AP=(a√3÷2)²and PA=(a÷6)²)
WE GET, AD²=28a²÷36
AD²=(7÷9)a²
AB=BC=CA=a
Therefore,9AD²=7AB2
HENCE PROVED