Question 536989
If m, m+1 and m+2 are the length of the sides of a right triangle,
they are all positive numbers and
the length of the hypotenuse is the largest number, m+2.
Then Pythagoras theorem says
{{{m^2+(m+1)^2=(m+2)^2}}} -->{{{2m^2+2m+1=m^2+4m+4}}}-->{{{m^2-2m-3=0}}} -->{{{(m+1)(m-3)=0}}} 
The solutions of the equation are {{{m=-1}}} and {{{m=3}}},
but since m must be positive, the only solution is {{{m=3}}}.
The triangle is a 3-4-5 triangle, corresponding to the best known of the Pythagorean triples (sets of 3 positive integers that can be sides of a right triangle).