1. **State the problem:** We have an isosceles triangle PQR with base RQ = 22 cm and height from P to midpoint M of RQ equal to 10 cm. We need to find the length of side PR. 2. **Recall the Pythagorean theorem:** In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Formula: $$c^2 = a^2 + b^2$$ where $c$ is the hypotenuse. 3. **Identify the right triangle:** The height PM is perpendicular to base RQ, so triangle PMR is right angled at M. 4. **Calculate half the base:** Since M is midpoint of RQ, $$RM = \frac{22}{2} = 11 \text{ cm}$$. 5. **Apply Pythagoras' theorem to triangle PMR:** $$PR^2 = PM^2 + RM^2 = 10^2 + 11^2 = 100 + 121 = 221$$ 6. **Find PR:** $$PR = \sqrt{221} \approx 14.866 \text{ cm}$$ 7. **Round to nearest centimetre:** $$PR \approx 15 \text{ cm}$$ **Final answer:** The length of side PR is approximately 15 cm.