Answer
3,4,5
Work Step by Step
The lengths of the triangle are consecutive positive integers.
Let the smallest side $=$ $x$,
The second side $=$ $x+1$
And the hypotenuse $=$ $x+2$.
Since they form a right-angled triangle, they follow Pythagoras Theorem. ie,
$x^{2}+ (x+1)^{2}$ $=$ $(x+2)^{2}$
Opening the brackets, we get
$x^{2}+x^{2}+2x+1$ $=$ $x^{2}+4x+4$
Combine the like terms,
$2x^{2}-x^{2}+2x-4x+1-4=0$
Solve the equation.
$x^{2}-2x-3=0$
Solve the quadratic for x by factorizing it.
$(x-3)(x+1)=0$
Thus $x=-1 , 3$
We can discard -1 because x cannot assume negative values.
Thus the sides of the triangle are
$x=3$
$x+1 = 4$
$x+2 =5$
