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Understand the map scale.

April 26, 2026Geography

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2 parts

\text{2.5 km}

\text{30 cm}

6 steps

What distance on land will be represented by a length of $5 \text{ cm}$ on a map of scale $1:50\,000$ ?

Understand the map scale.
A scale of $1:50\,000$ means that $1 \text{ unit on the map represents } 50\,000 \text{ units on the land}$ .
So, $1 \text{ cm on the map represents } 50\,000 \text{ cm on the land}$ .
Calculate the land distance for $5 \text{ cm}$ on the map.
$\text{Land distance} = \text{Map length} \times \text{Scale denominator}$ $\text{Land distance} = 5 \text{ cm} \times 50\,000$ $\text{Land distance} = 250\,000 \text{ cm}$
Convert the land distance to a more practical unit (kilometers).
Since $1 \text{ m} = 100 \text{ cm}$ and $1 \text{ km} = 1\,000 \text{ m}$ , then $1 \text{ km} = 100\,000 \text{ cm}$ .
$\text{Land distance in km} = \frac{250\,000 \text{ cm}}{100\,000 \text{ cm/km}}$ $\text{Land distance in km} = 2.5 \text{ km}$
The distance on land will be represented by a length of $5 \text{ cm}$ on the map is $\boxed{\text{2.5 km}}$ .

What length will a distance of $3 \text{ km}$ represent on a map of scale $1:10\,000$ ?

Understand the map scale.
A scale of $1:10\,000$ means that $1 \text{ unit on the map represents } 10\,000 \text{ units on the land}$ .
So, $1 \text{ cm on the map represents } 10\,000 \text{ cm on the land}$ .
Convert the land distance to centimeters.
$3 \text{ km} = 3 \times 1\,000 \text{ m} = 3\,000 \text{ m}$ $3\,000 \text{ m} = 3\,000 \times 100 \text{ cm} = 300\,000 \text{ cm}$
Calculate the map length.
$\text{Map length} = \frac{\text{Land distance}}{\text{Scale denominator}}$ $\text{Map length} = \frac{300\,000 \text{ cm}}{10\,000}$ $\text{Map length} = 30 \text{ cm}$
A distance of $3 \text{ km}$ will represent a length of $\boxed{\text{30 cm}}$ on the map.

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