Scale Drawings

A scale drawing represents a real object – a room, a building, a garden – on paper at a fixed, manageable size, using a stated scale like 1:100. Every length in the drawing has been shrunk (or occasionally enlarged) by exactly the same factor, so the drawing's proportions stay a perfectly faithful, true-to-life representation of the real thing.

Finding the Actual Length

Actual length = drawn length × scale factor.

A floor plan uses a scale of 1:50. A bedroom wall measures 8 cm on the plan. What is its actual length?

Actual length = 8 × 50 = 400 cm (4 metres).

Finding the Drawn Length

Using a scale of 1:50, how long should a 6-metre (600 cm) wall be drawn?

Drawn length = 600 ÷ 50 = 12 cm.

Real-Life Application

Architecture: floor plans and building elevations.
Interior design: furniture layouts drawn to scale before buying.
Engineering: technical drawings of machine parts.

Key Takeaways

A scale drawing represents every real measurement at the same fixed scale factor.
Multiply the drawn length by the scale factor to find the real length, and divide to go the other way.
Map scales, covered next, apply this exact same idea to geographic distances.

Practice: Scale Drawings

Find the Actual Length