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Solve scale drawing problems

Scale drawing problems involve interpreting a stated scale as a constant ratio between corresponding drawing lengths and actual lengths, then using proportional relationships to determine an unknown measurement in either representation. The learner maintains consistent units, distinguishes multiplicative scale factors from additive differences, and applies the relationship to maps, plans, and geometric figures; this treatment focuses on lengths and proportional reasoning, not formal similarity proofs or area and volume scaling.

Detailed Explanation: Solve scale drawing problems

A scale tells you how a length in a drawing compares with the actual length. It is a multiplicative relationship, not an amount to add.

For example, suppose a floor plan uses the scale

1 cm=4 m.1\text{ cm}=4\text{ m}.

This means every 11 centimeter on the drawing represents 44 meters in real life.

Example: A room is 6.56.5 cm long on the floor plan. How long is the actual room?

  1. Identify the scale and the drawing length.

1 cm⟶4 m1\text{ cm}\longrightarrow 4\text{ m} 6.5 cm⟶x m6.5\text{ cm}\longrightarrow x\text{ m}
  1. Set up a proportion. Match drawing lengths with actual lengths:

1 cm4 m=6.5 cmx m\frac{1\text{ cm}}{4\text{ m}}=\frac{6.5\text{ cm}}{x\text{ m}}
  1. Solve by multiplying the drawing length by the scale factor.

    Since 11 cm represents 44 m,

x=6.5×4=26x=6.5\times 4=26
  1. State the answer with units.

    The actual room is

26 meters long.\boxed{26\text{ meters long}}.

Check: 6.56.5 cm is 6.56.5 groups of 11 cm, so it represents 6.56.5 groups of 44 m, or 2626 m. Always keep the drawing and actual measurements matched correctly and use the units given by the scale.

Learn by doing: Solve scale drawing problems

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Metric Unit Scale on Map - Find Map Measurement - Power of 10 (to 1000000) - Change Unit


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