Question 455886
Let's the smaller leg = x m, then the other leg is (x+1) m and the hypotenuse is

{{{sqrt(x^2+(x+1)^2)}}}m.Since the perimeter is 12 m we write the equation:

{{{x+x+1+sqrt(x^2+(x+1)^2)=12}}}. We now solve this equation.

{{{sqrt(2x^2+2x+1)=11-2x}}}, squaring both sides we get:

{{{2x^2+2x+1=121-44x+4x^2}}}, set the equation to zero:{{{2x^2-46x+120=0}}},

divide both sides by 2 we get:{{{x^2-23x+60=0}}} solving this equation by 

factoring:{{{(x-3)(x-20)=0}}}. The roots are x=3 and x=20. We reject the solution 

x=20 because do not satisfy  our problem.

Answer:The lengths are:  3m, 4m, 5m.