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Explain what a bar scale and a number scale are, the meaning of the scale 1:50, and calculate the actual length and distance of a desk.

Mathematics

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Step-by-step solution

4 steps
  1. Solve 3.1.1

    • A bar scale is a graphic representation of the scale, usually a line segment divided into parts, with actual distances marked. It remains accurate even if the map or plan is resized.
    • A number scale (or ratio scale) is expressed as a ratio (e.g., 1:50) or a fraction. It indicates that one unit on the map represents a certain number of units in reality. It becomes inaccurate if the map or plan is resized.
  2. Solve 3.1.2

    The meaning of the scale 1:50 is that 1 unit of measurement on the plan represents 50 of the same units of measurement in actual length. For example, 1 cm on the plan represents 50 cm in reality.

  3. Solve 3.1.3

    The length of the desk on the plan is 6 cm. The scale is 1:50.
    To find the actual length, multiply the plan length by the scale factor.

    Actual length=Plan length×Scale factor\text{Actual length} = \text{Plan length} \times \text{Scale factor} Actual length=6 cm×50\text{Actual length} = 6 \text{ cm} \times 50 Actual length=300 cm\text{Actual length} = 300 \text{ cm}

    Convert the actual length from centimeters to meters (since 1 m = 100 cm):

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

    The actual length of the desk is 3 m\boxed{3 \text{ m}}.

  4. Solve 3.1.4

    The distance between the desks on the plan is 4 cm. The scale is 1:50.
    To find the actual distance, multiply the plan distance by the scale factor.

    Actual distance=Plan distance×Scale factor\text{Actual distance} = \text{Plan distance} \times \text{Scale factor} Actual distance=4 cm×50\text{Actual distance} = 4 \text{ cm} \times 50 Actual distance=200 cm\text{Actual distance} = 200 \text{ cm}

    Convert the actual distance from centimeters to meters (since 1 m = 100 cm):

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

    The actual distance between the desks is 2 m\boxed{2 \text{ m}}.

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