1. **Define the problem**: We know we have a side length b = 3, and the projection of b on the hypotenuse is given as 4.
2. **Use logic of geometry**: The projection must always be shorter than or equal to the side itself.
3. **Apply the contradiction**: The projection being greater than the side itself ( 4 > 3 ) directly indicates a fundamental contradiction.
4. **Conclusion**: Such a triangle does not exist in Euclidean geometry where the side projections violate the fundamental rules.