Question 501665
Yes you are correct.
Here's explanation:
Let X be the length of shorter leg
   Y be the length of longer leg
   Z be the length of hypotensue.

From the problem , we have
  Y = X + 1 ( longer leg is 1cm more than shorter leg)
  Z = X+ 2 (hypotenuse is 2cm longer than the shorter leg)

We know that
   X^2 + Y^2 = Z^2

Substituting values for Y and Z,
X^2 + (X+1)^2 = (X+2)^2
X^2 + X^2 + 2*X + 1 = X^2 + 4*X + 4
X^2 -2*X -3 = 0
X^2 -3X + X - 3 = 0
X(X-3) + 1(X-3)= =
(X-3)(X+1) = 0
X = 3, -1

Length should be positive.
Hence Shorter leg X = 3cm, Longer leg Y = 4cm and Hypotenuse Z = 5 cm