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Calculate the number scale of a store layout plan given the actual width is 4 m and assuming the drawn width is 2 cm.

Mathematics

ScanSolve AI Answer

Answer

1:200\text{1:200}

Step-by-step solution

4 steps
  1. State the given actual dimension.

    The actual width of Store Z is 4 m4 \text{ m}.

  2. Explain the need for measurement and state assumption.

    To derive the number scale, the width of Store Z on the layout plan must be measured from a physical copy. Since I cannot physically measure the image, I will assume that the width of Store Z on a printed version of the plan measures 2 cm2 \text{ cm}.

  3. Convert units for consistency.

    Convert the actual width to centimeters so it is in the same unit as the assumed drawn width:

    4 m=4×100 cm=400 cm4 \text{ m} = 4 \times 100 \text{ cm} = 400 \text{ cm}
  4. Calculate the number scale.

    The number scale is the ratio of the drawn width to the actual width:

    Scale=Drawn widthActual width\text{Scale} = \frac{\text{Drawn width}}{\text{Actual width}} Scale=2 cm400 cm\text{Scale} = \frac{2 \text{ cm}}{400 \text{ cm}} Scale=1200\text{Scale} = \frac{1}{200}

    This means that 1 cm1 \text{ cm} on the plan represents 200 cm200 \text{ cm} (or 2 m2 \text{ m}) in reality.

    The number scale used to draw this layout plan is 1:200\text{1:200}.

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