G2 · Solve practical scale and scale-diagram problems

Alberta Grade 11 Mathematics

Geometry

Use a drawing-to-real ratio to find lengths in plans, maps, and models.

What you will learn

• Explain what a scale tells you.
• Use a scale to find a real length or a drawing length.
• Keep units consistent and check whether an answer is reasonable.

Read the scale as a matching pair

• The first number describes the drawing; the second describes real life.
• Use the same unit on both sides of a scale ratio.

Choose a calculation that matches the question

• Drawing to real: multiply by the scale factor.
• Real to drawing: divide by the scale factor.
• Write units at each step so you can spot a mismatch.

Convert units and check the result

• Convert between centimetres, metres, and kilometres as needed.
• Compare the size of the answer with the scale and the situation.

Worked example

Find a walking distance from a map

1. Read the scale
   The map scale says each 1 cm on the map represents 25,000 cm in real life. Both lengths are in centimetres, so the scale can be used directly.
   $$1\text{ cm}:25{,}000\text{ cm}$$
2. Find the real distance
   The map length is 6.4 cm, so multiply by 25,000 to find the matching real length. The result is still in centimetres.
   $$6.4\times25{,}000=160{,}000\text{ cm}$$
3. Convert and check
   Convert centimetres to metres, then metres to kilometres. The result is plausible: a little over 6 cm on this map represents a distance a little over 1.5 km.
   $$160{,}000\text{ cm}=1{,}600\text{ m}=1.6\text{ km}$$

Worked example

Find room dimensions from a floor plan

1. Use the scale on each dimension
   Each drawing centimetre represents 50 real centimetres. Apply that same scale to both room measurements.
   $$8\times50=400\text{ cm},\quad 6.5\times50=325\text{ cm}$$
2. Convert to metres
   There are 100 centimetres in a metre. Divide each real measurement in centimetres by 100.
   $$400\text{ cm}=4\text{ m},\quad 325\text{ cm}=3.25\text{ m}$$
3. Check the dimensions
   The plan is longer in its first direction than its second, so the real room should have the same pattern. Both real dimensions are greater than the drawing dimensions, as expected for this scale.
   $$4\text{ m}>3.25\text{ m}$$

Worked example

Choose a drawing length for a workshop layout

1. Make the units match
   The scale compares the drawing and real lengths in the same unit. Convert the real length from metres to centimetres before dividing.
   $$2.4\text{ m}=240\text{ cm}$$
2. Find the plan length
   The real length is 30 times the drawing length, so divide the real length by 30 to find the drawing length.
   $$240\div30=8\text{ cm}$$
3. Check the scale direction
   The plan length should be smaller than the real length. Eight centimetres on the plan represents 240 centimetres in the workshop, which matches the scale.
   $$8\text{ cm}\times30=240\text{ cm}$$

Common mistakes and how to avoid them

Lesson summary

• A scale compares a drawing length with its real matching length.
• Multiply drawing length by the scale factor to find real length.
• Divide real length by the scale factor to find drawing length.
• Match units before calculating, then convert and check the answer.

Check your understanding

Key terms

Scale

A ratio that connects a length on a drawing with the matching real length.

Scale factor

The number of real units represented by one drawing unit.

Ratio

A comparison of two amounts.

Continue through Math 20-3

View the complete Math 20-3 Alberta Grade 11 Mathematics curriculum and lessons

• G1 · Solve problems involving two or three right triangles
• G3 · Model 3-D objects and draw their top, front, and side views
• G4 · Draw and describe simple exploded views and scaled components
• M2 · Solve volume and capacity problems with SI and imperial units
• N1 · Use and verify strategies for numerical puzzles and games
• N3 · Explain and calculate compound-interest growth

Tutor support for G2 · Solve practical scale and scale-diagram problems

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Alberta Grade 11 Mathematics (Math 20-3), expectation G2. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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