Is it possible for a right angled triangle with sides 3 and 4 units long to have a hypotenuse 6 units in length?

I am sure it isn’t but consider this: if you indent the hypotenuse with little stepped triangles the combined vertical and horizontal components will always add up to 7 units. As you make the triangles smaller and smaller this distance will tend towards 5 units in length as we learned in school. So the question is this. How can something 7 units in length tend towards 5 units in length without at some point being six units long?