SOLUTION: IN AN EQUILATERAL TRIANGLE ABC,AN IS PERPENDICULAR TO BC. PROVE THAT (AN)SQURE=3(BN)SQUARE.

Algebra ->  Pythagorean-theorem -> SOLUTION: IN AN EQUILATERAL TRIANGLE ABC,AN IS PERPENDICULAR TO BC. PROVE THAT (AN)SQURE=3(BN)SQUARE.      Log On


   

Question 795518: IN AN EQUILATERAL TRIANGLE ABC,AN IS PERPENDICULAR TO BC. PROVE THAT (AN)SQURE=3(BN)SQUARE.
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
For this triangle, Pythagorean theorem states that
(AN)^2 + (BN)^2 = (AB)^2
subtract (BN)^2 from both sides of =
(AN)^2 = (AB)^2 - (BN)^2
since triangle ABC is equilateral, perpendicular segment AN to BC bisects line segament BC, therefore
AB = 2BN and
(AN)^2 = (2BN)^2 - (BN)^2
(AN)^2 = 4(BN)^2 - (BN)^2
(AN)^2 = 3(BN)^2