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17 October, 16:56

Determine a distance from a given map on a map of 1:50000 and the ground distance=7.5km calculate the distance on the map in centimeter using the formula below 1/50000=?/7.5km

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  1. 17 October, 18:10
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    The distance on the map=15 cm

    Explanation:

    Scaling is a way of converting actual measurements to map measurements. Scales can be written in form of ratios, for example 1:2 or in form of 1 cm representing 2 km. In the latter case, the units are always in centimeters.

    In the case above, the scale 1:50,000 generally implies that 1 centimeter unit on the map represents 50,000 centimeter units on the ground. The expression for determining the map measurements is;

    M=S. F*G

    where;

    M=map measurements

    S. F=scale factor

    G=ground measurements

    In our case;

    M=unknown

    S. F=1/50,000

    G=7.5 km, convert to meters

    1 km=1,000 km

    7.5 km=?

    G=7.5*1,000=7,500 m

    1 m=100 cm

    7,500 m=?

    G=7,500*100=750,000 cm

    replacing;

    M = (1/50,000) * 750,000=15 cm

    The distance on the map=15 cm
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