Question 544919
Let the legs be x & x+1

The diagonal & sides form a right triangle

By Pythagoras theorem 							
Hypotenuse^2 = Leg1^2+leg2^2	
5^2=x^2+(x+1)^2

25=x^2+x^2+2x+1
2x^2+2x-34=0
/2
x^2+x-12=0
x^2+4x-3x+12=0
x(x+4)-3(x+4)=0
(x+4)(x-3)=0
x= 3 the positive value
the other leg is 3+1= 4

The sides are 3,4,5