The-sides-of-a-triangle-are-of-lengths-m-2-n-2-m-2-n-2-2mn-Show-that-it-is-a-right-angle-

Question Number 19783 by NECC last updated on 15/Aug/17

T h e s i d e s o f a t r i a n g l e a r e o f

l e n g t h s \sqrt{(m^{2} - n^{2})}, m^{2} + n^{2}, 2 m n .

S h o w t h a t i t i s a r i g h t a n g l e Δ .

Commented by Tinkutara last updated on 15/Aug/17

Right triangle is not possible with these

sides .

Commented by NECC last updated on 15/Aug/17

p l e a s e p r o v e y o u r s t a t e m e n t

m a t h e m a t i c a l l y .

Commented by Tinkutara last updated on 15/Aug/17

Since m^{2} - n^{2} + 4 m^{2} n^{2} \neq m^{4} + n^{4} +

2 m^{4} n^{4} . Hence right triangle is not

possible .

Answered by Rasheed.Sindhi last updated on 15/Aug/17

{(m^{2} - n^{2})}^{2} + {(2 mn)}^{2}

= m^{4} - {2 m}^{2} n^{2} + n^{4} + {4 m}^{2} n^{2}

= m^{4} + {2 m}^{2} n^{2} + n^{4}

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

Hence rightangle triangle .

Commented by Tinkutara last updated on 15/Aug/17

But the side is \sqrt{m^{2} - n^{2}} . Its square

will be m^{2} - n^{2} only . (OK, it can be

considered a typing error in the

question)

Commented by NECC last updated on 16/Aug/17

t h a n k s \dots . i t s c l e a r n o w .

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