in triangle BAC ,angle c=90 and q is mid point of bc.prove that AB square =4AQ square-3AC square

Asked by Pranav Limbani | 4th Sep, 2012, 06:59: PM

Expert Answer:

Answer : Given : in triangle bac ,angle c=90 and q is mid point of bc.
To prove :ab2  =4aq2 - 3ac2

Now let us take RHS of the proving statement, we get
4aq2 - 3ac2
= 4(qc2+ac2)- 3ac2  {using pythagorus theorm in triangle qac}
4qc2+ac
= 4 (bc/2)2 +ac2 { since q is mid point of side bc ,qc= bc/2}
= bc2 + ac2
= ab2 {using pythagorus theorm in triangle bac } 
= LHS
hence proved 

Answered by  | 5th Sep, 2012, 12:11: AM

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