1. The problem asks where the value 175 comes from in the calculation of the first moment $Q_b$. 2. The first moment $Q_b$ is calculated as $$Q_b = 2(150)(60 \times 100) + (175)(300 \times 60)$$ where 175 is a distance measurement. 3. In the beam cross-section, the number 175 represents the vertical distance from the centroidal x-axis to the centroid of the larger red-shaded rectangular area in part (b). 4. This distance is found by adding the heights of the smaller boards below the red area to reach the centroid of the red area. 5. Specifically, 175 mm is the sum of 150 mm (height of the lower boards) plus half of the height of the red-shaded area (60 mm), so: $$175 = 150 + \frac{60}{2}$$ 6. This distance is used to calculate the first moment of area because the first moment is the area times the distance from the centroidal axis. 7. Therefore, 175 mm is the vertical distance from the centroidal x-axis to the centroid of the red-shaded area in part (b).