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Explain different types of scales used in maps and plans. Then, calculate the actual length of a desk and the distance between desks given their representation on a plan with a scale of 1:50.

Geography

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3.1.1

  • A bar scale (or graphic scale) shows the scale visually as a line segment divided into units, allowing direct measurement on the plan.
  • A number scale (or ratio scale) expresses the scale as a ratio (e.g., 1:50) or a fraction, indicating that one unit on the plan represents a certain number of units in reality.

3.1.2
The scale 1:50 means that 1 unit of measurement on the plan represents 50 of the same units of measurement in actual size. For example, 1 cm on the plan corresponds to 50 cm in reality.

3.1.3

  1. Determine the actual length in centimeters.

    The desk measures 6 cm on the plan, and the scale is 1:501:50.

    Actual length in cm=6 cm×50=300 cm\text{Actual length in cm} = 6 \text{ cm} \times 50 = 300 \text{ cm}
  2. Convert the actual length from centimeters to meters.

    Since 1 m=100 cm1 \text{ m} = 100 \text{ cm}:

    Actual length in m=300 cm100 cm/m=3 m\text{Actual length in m} = \frac{300 \text{ cm}}{100 \text{ cm/m}} = 3 \text{ m}

    The actual length of the desk in metres is:

    3 m\boxed{3 \text{ m}}

    3.1.4

  3. Determine the actual distance in centimeters.

    The desks are 4 cm apart on the plan, and the scale is 1:501:50.

    Actual distance in cm=4 cm×50=200 cm\text{Actual distance in cm} = 4 \text{ cm} \times 50 = 200 \text{ cm}
  4. Convert the actual distance from centimeters to meters.

    Since 1 m=100 cm1 \text{ m} = 100 \text{ cm}:

    Actual distance in m=200 cm100 cm/m=2 m\text{Actual distance in m} = \frac{200 \text{ cm}}{100 \text{ cm/m}} = 2 \text{ m}

    The actual distance between the two learners' desks in metres is:

    2 m\boxed{2 \text{ m}}
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