Scale drawings and maps

Using scale ratios on maps and plans to find real distances and drawing lengths, and finding the scale factor.

Scales

A scale of $1 : 50\,000$ means $1$ unit on the map is $50\,000$ of the same units in real life. The scale factor is $50\,000$.

Example 1●

On a $1 : 50\,000$ map, two towns are $6$ cm apart. Find the real distance in km.

$6 \times 50\,000 = 300\,000$ cm

$= 3000$ m $= 3$ km

Example 2●●

A $12$ m room is drawn $4$ cm long on a plan. Find the scale.

$4$ cm $: 12$ m $= 4 : 1200$

$= 1 : 300$

Flashcards

Scale 1 : 100

1 cm on the plan is 1 m in real life.

Real length

drawing length × scale factor

cm in a km

$100\,000$

Practice

On a $1 : 50\,000$ map, towns are $6$ cm apart. Real distance in km?
A $12$ m room is $4$ cm on a plan. Write the scale like 1:200.
Scale $1 : 100$. A wall is $5$ cm on the plan. Real length in metres?
Scale $1 : 200$. A $16$ m fence is how many cm on the plan?
Scale $1 : 250\,000$. $5$ cm on the map is how many km?
A model car is built at $1 : 20$. The real car is $4$ m long. How many cm is the model?
Which scale shows the most detail?
$4$ cm on a map is $1$ km. What is the scale factor?