Note that we don't need to know how high the plane is.

We know the initial speed and we know the final speed. We know that the acceleration is constant. If we knew the acceleration we could find the distance along the slide using the formula:

v^2 = v0^2 + 2a(x - x0).

Rule of thumb: If you don't know an acceleration, do a Newton's 2nd Law problem. So, set up a Free-Body-Diagram. I've got a coordinate system where +x is down the incline and +y is directed perpendicular to and upward from the incline. The object has a weight, w, directed downward. It also has a normal force, N, acting in the +y direction. Friction is not mentioned in the problem, nor implied in any way, so assume we can ignore this.

Newton's 2nd Law in the +x direction is:

(Sum)Fx = w*sin(theta) = ma (Where "theta" is the angle of incline.)

Make sure you understand why we are using sine here and not cosine!

w = mg, so

mg*sin(theta) = ma

a = g*sin(theta).

You now have the acceleration, so you can now use the v^2 formula above to solve for x.

-Dan