Question

Find the general formula for three integers which may be taken to represent the lengths of the sides of a right angled traingle.

• A. $2m^2-n^2,3mn,2m^2+n^2$
• B. $2m^2-n^2,2mn,m^2+n^2$
• C. $m^2-n^2,2mn,m^2+n^2$
• D. None of these

Answer 1

The correct option is C $m^2-n^2,2mn,m^2+n^2$

Let a,b,c be sides of triangle

$c^2=a^2+b^2$

Let $a=x+y,b=x-y$

$\therefore c^2={(x+y)}^2+{(x-y)}^2$

$c^2=4xy$

$c=2\sqrt{xy}$

Let $x=m^2,y=n^2$

$\therefore a=m^2+n^2,b=m^2-n^2,c=2mn$ is general solutions of sides of right angled triangle.