This is a scale map of an actual campus.

Start by finding the scale of this map. At the actual campus, one side length of the dining hall is 50 m. On the scale map, it is 25 cm. What is the scale?
A scale map of a campus with dimensions 40 cm by 20 cm. Within the campus are a parking lot and a dining hall. One side length of the dining hall is labeled 25 cm.
Scale: 1 cm =
m

1 answer

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:

\[ \text{Scale: } 1 \text{ cm} = 2 \text{ m} \]