Call the legs a and b.
But b=a+1 and hypotenuse=b+2=a+3, so
(a+3)^2=a^2+(a+1)^2; a^2+6a+9=a^2+a^2+2a+1 (by Pythagoras).
From this we can collect terms together: a^2-4a-8=0.
We can write a^2-4a=8 and add 4 to each side: a^2-4a+4=12:
(a-2)^2=12 and now take square root of each side:
a-2=√12=2√3 (positive square root only because the sides are all positive lengths).
So a=2+2√3, b=3+2√3 and hypotenuse=5+2√3 (all measurements are mm).
Approximately, a=5.464mm, b=6.464mm and hypotenuse=8.464mm.