On a topographical map with a Representative Fraction (RF) of 1 : 50,000, a straight coast… — JAMB UTME

On a topographical map with a Representative Fraction (RF) of $1 : 50,000$ , a straight coastline segment between two coastal lighthouses measures $14.4\text{ cm}$ . What is the actual ground distance between the two lighthouses in kilometers?

Answer: 7.2 km

Answer

The actual ground distance between the two lighthouses is 7.2 km.

To find actual ground distance from a Representative Fraction (

1 : 50,000

), multiply the measured map distance (

14.4\text{ cm}

) by the scale denominator (

50,000

) to get

720,000\text{ cm}

. Converting to kilometers by dividing by

100,000

yields

7.2\text{ km}

Step-by-Step Solution

Calculate the ground distance in centimeters using the Representative Fraction denominator.

14.4\text{ cm} \times 50,000 = 720,000\text{ cm}

The scale ratio

1 : 50,000

means

1\text{ cm}

on the map represents

50,000\text{ cm}

on the ground.

Convert the ground distance from centimeters to meters.

720,000\text{ cm} \div 100 = 7,200\text{ m}

There are

100\text{ cm}

1\text{ meter}

Convert the ground distance from meters to kilometers.

7,200\text{ m} \div 1,000 = 7.2\text{ km}

There are

1,000\text{ meters}

1\text{ kilometer}

Key Concept

Converting map distance to actual ground distance using Representative Fraction (RF) scale

Estimated Time:1m 0s

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