Question

In triangle abc bd:cd=3:1 and ad perpendicular to bc.Prove that 2(ab

Answer 1

 



Sheetal asked in Math 

... of triangle ABC is an acute angle and AD perpendicular to BC ...

Applying Pythagoras theorem in ΔADB, we obtain

AD2 + DB2 = AB2

⇒ AD2 = AB2 − DB2 … (1)

Applying Pythagoras theorem in ΔADC, we obtain

AD2 + DC2 = AC2

AB2 − BD2 + DC2 = AC2 [Using equation (1)]

AB2 − BD2 + (BC − BD)2 = AC2

AC2 = AB2 − BD2 + BC2 + BD2 −2BC × BD

= AB2 + BC2 − 2BC × BD