1. **Problem Statement:** We have three scale drawings of a prism: front view (6 units wide by 6 units tall), side view (8 units wide by 3 units tall), and plan view (8 units wide by 3 units tall). The 3D drawing shows an L-shaped prism with a bottom horizontal length of 25 cm, and two missing lengths: a top horizontal length and a vertical height. 2. **Understanding the Views:** - The front view shows height and width (6 units by 6 units). - The side and plan views both show the depth and height (8 units by 3 units). 3. **Relating Scale Units to Actual Lengths:** - The bottom horizontal length in the 3D drawing corresponds to the total width from the front view, which is 6 units. - The bottom length is given as 25 cm, so each unit in width corresponds to $$\frac{25}{6}$$ cm. 4. **Finding the Missing Top Horizontal Length:** - The top horizontal length corresponds to the difference in width between the front view and the side view projections. - From the front view, width is 6 units; from the side view, depth is 8 units. - The L-shape means the top horizontal length is the difference between the total width (6 units) and the width of the side segment (which corresponds to 8 units depth). - However, since the side view width is 8 units and the front view width is 6 units, the top horizontal length corresponds to the side view width (8 units) minus the front view width (6 units), but this is not possible since 8 > 6. - Instead, the bottom horizontal length (25 cm) corresponds to the sum of the two horizontal segments in the L-shape: the bottom segment (given as 25 cm) and the top segment (missing). 5. **Calculating the Missing Top Horizontal Length:** - The total horizontal length in the plan view is 8 units. - The bottom horizontal segment corresponds to 6 units (from front view width). - So, the missing top horizontal length corresponds to $$8 - 6 = 2$$ units. - Using the scale from bottom segment: 6 units = 25 cm, so 1 unit = $$\frac{25}{6}$$ cm. - Therefore, missing top horizontal length = $$2 \times \frac{25}{6} = \frac{50}{6} = 8.33$$ cm (approx). 6. **Finding the Missing Vertical Length:** - The vertical height corresponds to the height difference between the front view and the side view. - Front view height is 6 units; side view height is 3 units. - The missing vertical length is the difference: $$6 - 3 = 3$$ units. - We need to find the scale for height. 7. **Calculating the Scale for Height:** - From the side view, height is 3 units. - The side view height corresponds to the vertical segment in the 3D drawing. - Since the side view height is 3 units, and the front view height is 6 units, the missing vertical length corresponds to 3 units. - Using the scale from the front view height: 6 units correspond to an unknown length, but since the bottom horizontal length scale is $$\frac{25}{6}$$ cm per unit, we assume the same scale applies vertically. - So, missing vertical length = $$3 \times \frac{25}{6} = \frac{75}{6} = 12.5$$ cm. **Final answers:** - Missing top horizontal length = 8.33 cm (approx). - Missing vertical length = 12.5 cm. These lengths should be written on the 3D drawing accordingly.