1. **State the problem:** We have a beam AB of length 10 ft with a trapezoidal distributed load starting at 120 lb/ft at A and increasing linearly to 280 lb/ft at B. We need to find the magnitude and position of the resultant load. 2. **Identify the load distribution:** The load intensity increases linearly from 120 lb/ft at A to 280 lb/ft at B over 10 ft. The load forms a trapezoid with bases 120 lb/ft and 280 lb/ft and height 10 ft. 3. **Calculate the magnitude of the resultant load:** The magnitude is the area under the load distribution curve. $$\text{Resultant load } R = \frac{(120 + 280)}{2} \times 10 = \frac{400}{2} \times 10 = 200 \times 10 = 2000 \text{ lb}$$ 4. **Calculate the position of the resultant load:** The centroid of a trapezoid from the left end is given by $$\bar{x} = \frac{h}{3} \times \frac{2a + b}{a + b}$$ where $a = 120$, $b = 280$, and $h = 10$ ft. Calculate: $$\bar{x} = \frac{10}{3} \times \frac{2 \times 120 + 280}{120 + 280} = \frac{10}{3} \times \frac{240 + 280}{400} = \frac{10}{3} \times \frac{520}{400} = \frac{10}{3} \times 1.3 = 4.333 \text{ ft}$$ 5. **Interpretation:** The resultant load of 2000 lb acts 4.333 ft from point A towards B. **Final answer:** - Magnitude of resultant load: $2000$ lb - Position from A: $4.333$ ft