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11 December, 22:56

The scale on the map is stated as 1 : 200000. A main road connects two towns which are 28 kilometres apart. How far will it be on the map, in centimetres, between the two towns along the main road

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  1. 11 December, 23:07
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    The distance on the map between the two towns=14 cm

    Step-by-step explanation:

    Step 1

    Express the scale as;

    1:200,000 this means that 1 cm on the map represents 200,000 cm on the road, 1 cm:200,000 cm

    Step 2

    Convert 28 kilometers to m

    1 meter=1,000 kilometers

    28 kilometers=28*1,000=28,000 meters

    Convert 28,000 meters to centimeters

    1 meter=100 centimeters

    28,000 meters=28,000*100=2,800,000 centimeters

    Step 3

    Using the scale factor of 1:200,000 convert 2,800,000 cm on the road can be converted to map measurements as follows;

    Distance on the map=scale factor*distance on the road

    where;

    scale factor=1/200,000

    distance on the road=2,800,000 cm

    replacing;

    Distance on the map = (1/200,000) * 2,800,000

    Distance on the map=14 cm

    The distance on the map between the two towns=14 cm
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