A regional planning map with a statement scale of 2\text{ cm to } 5\text{ km} is enlarged … — JAMB UTME

A regional planning map with a statement scale of $2\text{ cm to } 5\text{ km}$ is enlarged so that its linear dimensions are increased by a factor of $2.5$ . If the distance between two agricultural centers on the enlarged map measures $16\text{ cm}$ , what is the actual ground distance between them?

A
$6.4\text{ km}$
$16.0\text{ km}$ Answer
C
$40.0\text{ km}$
D
$100.0\text{ km}$

Answer

The actual ground distance between the two agricultural centers is

16.0\text{ km}

The original statement scale of

2\text{ cm to } 5\text{ km}

simplifies to

1\text{ cm to } 2.5\text{ km}

. Enlarging the map's linear dimensions by a factor of

2.5

means that details become

2.5

times larger, so

1\text{ cm}

on the new map represents

\frac{2.5\text{ km}}{2.5} = 1.0\text{ km}

. Therefore, a measured distance of

16\text{ cm}

on the enlarged map corresponds to

16\text{ cm} \times 1.0\text{ km/cm} = 16.0\text{ km}

on the ground.

Step-by-Step Solution

Determine the unit scale of the original map.

Since

2\text{ cm}

represents

5\text{ km}

1\text{ cm}

represents

\frac{5\text{ km}}{2} = 2.5\text{ km}

Establishing the distance represented by

1\text{ cm}

on the original map provides the baseline linear scale.

Calculate the new linear scale after map enlargement.

The new scale denominator is

\frac{2.5\text{ km}}{2.5} = 1.0\text{ km}

per centimeter (

1\text{ cm to } 1\text{ km}

Enlarging a map by a linear factor of

2.5

means each centimeter on the new map represents a smaller ground distance by a factor of

2.5

Compute the actual ground distance using the enlarged map measurement.

\text{Ground Distance} = 16\text{ cm} \times 1.0\text{ km/cm} = 16.0\text{ km}.

Multiplying the measured distance on the enlarged map by the new ground equivalence yields the total actual distance.

Key Concept

Map Scale Conversion during Linear Enlargement

Estimated Time:2m 0s

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