1. **State the problem:** We need to find the height of a 3D triangular prism. The prism has a right triangle as its base with sides 2 inches and 4 inches meeting at a right angle, and the prism's length (height) is 5 inches. 2. **Identify the height of the prism:** In a triangular prism, the height is the length perpendicular to the base triangle, which is given as 5 inches. 3. **Clarify the base triangle:** The base triangle has legs 2 inches and 4 inches, and the hypotenuse is 3 inches (which seems inconsistent with the Pythagorean theorem, but since the problem states it, we accept it as given). 4. **Conclusion:** The height of the prism is the length of the prism, which is 5 inches. **Final answer:** $$\text{Height of the prism} = 5 \text{ inches}$$