1. **Problem statement:** We have a right-angled triangle PQR with the right angle at R. The hypotenuse PQ is 50 cm, and one leg QR is 48 cm. We need to find the length of the other leg PR. 2. **Formula used:** According to Pythagoras' theorem, in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: $$PQ^2 = PR^2 + QR^2$$ 3. **Substitute known values:** $$50^2 = PR^2 + 48^2$$ 4. **Calculate squares:** $$2500 = PR^2 + 2304$$ 5. **Isolate $PR^2$:** $$PR^2 = 2500 - 2304$$ 6. **Simplify:** $$PR^2 = 196$$ 7. **Find $PR$ by taking the square root:** $$PR = \sqrt{196}$$ 8. **Calculate the square root:** $$PR = 14$$ **Final answer:** The length of PR is 14 cm.