On a topographical map drawn to a scale of 1 : 50,000, the straight-line distance between … — JAMB UTME

On a topographical map drawn to a scale of $1 : 50,000$ , the straight-line distance between Town X and Town Y is measured as $8\text{ cm}$ . What is the actual ground distance between the two towns in kilometers?

Answer: 4 km

Answer

The actual ground distance between Town X and Town Y is

4\text{ km}

To determine the actual ground distance, multiply the measured map distance (

8\text{ cm}

) by the representative scale ratio denominator (

50,000

), giving

400,000\text{ cm}

. Dividing this by

100,000

converts the distance into kilometers, yielding

4\text{ km}

Step-by-Step Solution

Calculate the ground distance in centimeters using the map scale denominator.

Ground distance in cm =

8\text{ cm} \times 50,000 = 400,000\text{ cm}

A Representative Fraction of

1 : 50,000

indicates that

1\text{ unit}

on the map represents

50,000\text{ units}

of the same measurement on the actual ground.

Convert centimeters into kilometers.

Ground distance in km =

\frac{400,000}{100,000} = 4\text{ km}

Since

1\text{ m} = 100\text{ cm}

and

1\text{ km} = 1,000\text{ m}

1\text{ km}

contains

100,000\text{ cm}

Key Concept

Ground distance calculation using Representative Fraction (RF) scale

Estimated Time:45s

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