1. **State the problem:** We have a right triangle PQR with sides PQ = 20, QR = 21, and PR = 13. The height $h$ is drawn from the top vertex P perpendicular to the base QR. We need to find the value of $h$. 2. **Identify the right angle:** Since the triangle is right-angled, the Pythagorean theorem applies. We check which side is the hypotenuse by comparing the squares: $$20^2 = 400, \quad 21^2 = 441, \quad 13^2 = 169$$ The largest side is QR = 21, so the right angle is at P or R. But since height $h$ is drawn from P to QR, P is the vertex opposite QR, so QR is the hypotenuse. 3. **Use the formula for the height to the hypotenuse in a right triangle:** The height $h$ from the right angle vertex to the hypotenuse is given by $$h = \frac{\text{product of the legs}}{\text{hypotenuse}}$$ Here, the legs are PQ and PR, and the hypotenuse is QR. 4. **Calculate $h$:** $$h = \frac{PQ \times PR}{QR} = \frac{20 \times 13}{21} = \frac{260}{21}$$ 5. **Simplify the fraction if possible:** 260 and 21 have no common factors other than 1, so $$h = \frac{260}{21} \approx 12.38$$ **Final answer:** $$h = \frac{260}{21} \approx 12.38$$