1. **Problem Statement:** We have a right triangle WZX with a right angle at W. An altitude WY is drawn to the hypotenuse ZX, meeting at Y. Given WY = 4 units, ZY = 3 units, and we want to find the length of side WZ = c. 2. **Key Concept:** In a right triangle, the altitude to the hypotenuse creates two smaller right triangles that are similar to the original triangle and to each other. This similarity allows us to use geometric mean relationships. 3. **Formula:** The altitude WY satisfies the relation: $$WY^2 = ZY \times YX$$ where ZY and YX are the segments into which the hypotenuse is divided by the altitude. 4. **Given:** WY = 4, ZY = 3, so: $$4^2 = 3 \times YX$$ $$16 = 3 \times YX$$ 5. **Solve for YX:** $$YX = \frac{16}{3}$$ 6. **Find hypotenuse ZX:** $$ZX = ZY + YX = 3 + \frac{16}{3} = \frac{9}{3} + \frac{16}{3} = \frac{25}{3}$$ 7. **Use similarity to find side WZ = c:** The side WZ corresponds to segment ZY on the hypotenuse, and WX corresponds to YX. Using the similarity ratio: $$\frac{WZ}{ZY} = \frac{ZX}{WZ}$$ Cross-multiplied: $$WZ^2 = ZY \times ZX$$ 8. **Calculate:** $$c^2 = 3 \times \frac{25}{3} = 25$$ 9. **Find c:** $$c = \sqrt{25} = 5$$ **Final answer:** The value of side c is 5 units.