Find the distance from the gate to the shed (the distance between the two closest points in a straight line) in meters.

Explanation:

We need to find the straight-line distance between the gate and the shed on the plan, using the scale where each cell side is 2 meters.

Step-by-step solution:

1. Locate the gate on the plan. The entrance/exit is through the gate, which is implied to be at the edge of the property, near the garage (marked as 7).
2. Locate the shed on the plan. The shed is described as being located next to the garage. On the plan, the shed is marked with the number 4.
3. Determine the coordinates of the gate and the shed. Let's assume the bottom-left corner of the property is (0,0). The gate is at the entrance. The garage (7) is to the right of the entrance, and the shed (4) is next to it. Let's consider the garage as being at coordinates (x_g, y_g) and the shed at (x_s, y_s). From the plan, the garage (7) is 3 cells away from the left edge, and the shed (4) is 1 cell to the right of the garage. Let's estimate the gate is at the beginning of the driveway, let's say at cell coordinate (0,0) in relation to the driveway. The garage (7) is at approximately (6m, 0m) relative to the start of the driveway. The shed (4) is adjacent to the garage, let's say at (8m, 0m) relative to the start of the driveway.
4. The problem statement says 'При входе на участок справа от ворот находится баня, а слева гараж, отмеченный на плане цифрой 7.' This means garage (7) is to the left of the entrance. Let's re-evaluate coordinates. Let the entrance (gate) be at origin (0,0). Then the garage (7) is to the left, let's say at (-6, 0). The shed (4) is next to the garage, so at (-8, 0). However, the diagram shows the garage (7) and shed (4) to the right of the entrance. Let's assume the entrance is at the bottom edge. The garage (7) is 3 units to the right, and the shed (4) is 1 unit further right. So, if the entrance is at (0,0), the garage (7) is at (6,0) and the shed (4) is at (8,0). This aligns with the visual representation.
5. Calculate the distance between the gate (0,0) and the shed (8,0). This is a horizontal distance.
6. Distance = sqrt((x2-x1)^2 + (y2-y1)^2) = sqrt((8-0)^2 + (0-0)^2) = sqrt(8^2) = 8 meters.
7. The distance between the gate and the shed is 8 meters.

Answer: 8