Question

prove that triangle ABC is right angled at A if AB=2n+1, BC=2n(n+1)+1

Answer 1

Step-by-step explanation:

if ABC is right angled at A then it must follow pythagoras theorem

given AB=2n+1

AC=2n(n+1)

BC=2n (n+1)+1

to prove

AB^2 +AC^2 =BC^2

LHS={2n+1}^2 +{2n (n+1)}^2=(4n^2 +1 +4n )+{4n^2 (n^2 +2n+1)}

=4n^4 +8n^3 +8n^2+4n+1

RHS

={2n(n+1)+1}^2

={4n^4 +8n^3 +4n^2 +1+4n^2 +4n}

=4n^4 +8n^3 +8n^2 +4n+1

we got LHS=RHS

pythagoras theorem is satisfied

so ABC is right angled at A