Do the following lengths form a right triangle ?

Answer:
Yes.
Step-by-step explanation:
If you can fit them in the Pythagorean theorem equation and make the equation true, then they do form a right triangle.
one leg length = 5
other leg length = 12
hypotenuse length = 13
The Pythagorean theorem equation is
a^2 + b^2 = c^2
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
5^2 + 12^2 = 13^2
25 + 144 = 169
169 = 169
Since the lengths do make the equation true, the three lengths do form a right triangle.