1. **State the problem:** We have a right triangle PQR with a right angle at R. The hypotenuse PQ measures 37 cm, and one leg RQ measures 35 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: $$PQ^2 = PR^2 + RQ^2$$ 3. **Substitute known values:** $$37^2 = PR^2 + 35^2$$ 4. **Calculate squares:** $$1369 = PR^2 + 1225$$ 5. **Isolate $PR^2$:** $$PR^2 = 1369 - 1225$$ 6. **Simplify:** $$PR^2 = 144$$ 7. **Find $PR$ by taking the square root:** $$PR = \sqrt{144} = 12$$ **Final answer:** The length of side PR is 12 cm.