Question

Hi I am CURIE EVANGALINE
Plz... Help me.....


IN AN EQUILATERAL TRIANGLE ABC , AD IS PERPENDICULAR TO BC, PROVE THAT AD3=3BD2(ad cube = 3× bd square)

Answer 1

hey dear!
question is wrong it not AD^3 it must be AD^2
ABD is a right triangle
then,
AD^2 + BD^2 =AB^2 (BY PYTHA.)
ALL side in eq triangle are equal and D point divide BC in equal parts
THUS ,
BD=1/2 BC
AB=2BD
THEN, AD^2= (2BD)^2 +BD^2
AD^2= 3BD^2

method 2

tanB=AD/BD
B=60°
root3 =AD/BD
then ,
AD=root3 BD
take square on both side
AD^2=3BD^2
Hence proved
sweety!!!