To find the scale of the map, we start by comparing the actual size of the dining hall to its representation on the scale map.
Given:
- The actual length of one side of the dining hall: 50 m
- The corresponding length on the scale map: 25 cm
First, we convert the actual size of the dining hall from meters to centimeters, since the scale map dimensions are in centimeters. There are 100 centimeters in one meter:
\[ 50 \text{ m} = 50 \times 100 \text{ cm} = 5000 \text{ cm} \]
Next, we can set up the scale ratio by comparing the actual length to the length on the map:
\[ \text{Scale} = \frac{\text{Length on the map}}{\text{Actual length}} = \frac{25 \text{ cm}}{5000 \text{ cm}} = \frac{25}{5000} = \frac{1}{200} \]
This means that 1 cm on the map represents 200 cm in reality.
To express this relationship in terms of meters, we convert 200 cm to meters:
\[ 200 \text{ cm} = \frac{200}{100} \text{ m} = 2 \text{ m} \]
Therefore, the scale of the map can be stated as:
\[ \text{Scale: } 1 \text{ cm} = 2 \text{ m} \]