Scale drawings: word problems

Key notes:

1️⃣ What is a Scale Drawing? 📏🖌️

  • A scale drawing is a representation of an object or area where all dimensions are proportional to the real object.
  • Example: A map showing a city where 1 cm = 1 km. 🌍

2️⃣ Understanding Scale 🔍

  • Scale shows the ratio between the drawing and the actual object.
  • Common formats:
    • Ratio: 1:50 (1 unit on drawing = 50 units in real life)
    • Fraction: 1/50
    • Verbal: “1 cm represents 50 cm”

3️⃣ Word Problems with Scale Drawings 📝🤔

To solve word problems:

  • Identify the scale 🎯
  • Decide what is being asked ❓
  • Write a proportion:

length on drawing/actual length = scale ratio

  • Solve for the missing value ✏️

4️⃣ Example Problem 🌈

Problem: A garden is 150 m long. On a map, the scale is 1:1000. How long is the garden on the map?

Solution:

length on mapa/ctual length=1/1000

Length on map = 150/1000 = 0.15 m =15 cm📐

5️⃣ Tips & Tricks 💡

  • ✅ Always convert units to match the scale.
  • ✅ Draw a small diagram if it helps visualize.
  • ✅ Remember: Scale ratio = drawing ÷ actual.
  • ✅ Check if the question asks for drawing length or actual length.

6️⃣ Fun Emoji Reminder 🎉

  • 🖌️ Drawing length → use map or plan
  • 📏 Actual length → real-life measurement
  • 🔄 Use proportions to convert!

Learn with an example

🔔 Ayana measured a swimming pool and made a scale drawing. The scale she used was 7 centimetres : 3 metres. The pool is 28 centimetres in the drawing. How wide is the actual pool?

Write the scale of the drawing as a fraction:

7cm /3m

Write an equivalent fraction with 28 centimetres as the numerator.

7cm × 4 /3m × 4 =28 cm / 12 m

The actual pool is 12 metres wide.

🔔 Pablo wants to check out a book from his local library, but it is not available. Pablo decides to visit the library in Wildgrove to see if that location has a copy of the book. On a map, the two libraries are 48 centimetres apart. If the scale of the map is 1 centimetre : 1 kilometre, then what is the actual distance between the two libraries?

Write a ratio that represents the scale of the map in centimetres to
kilometres: 1/1.

Write a ratio that relates the centimetres between the two libraries on the
map to the kilometres between the two libraries in real life: 48/d.

Use those ratios to set up a proportion and solve.

1/1 = 48/d

Multiply both sides by d.

1/1 xd = 48/d xd

Simplify
d = 48
The actual distance between the two libraries is 48 kilometres.


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🔔 On a public transportation map, two stations are 7 centimetres apart, whereas in real life the distance between them is 7 kilometres. What scale does the map use?

1 centimetre = _______ kilometres

Write a ratio that relates the centimetres between the two stations on the map to the

kilometres between the two stations in real life: 7/7 ,

To find the scale of the map, rewrite this ratio with 1 in the numerator.

7/7 = 1/1 Divide the numerator and denominator by 7

The map uses a scale of 1 centimetre = 1 kilometre.

Let’s Practice!