on a map of scale 1:20000 the area of forest is 50 cm sq. On another map the area of forest is 8cm sq .find the scale of the second map.

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william1941 | College Teacher | (Level 3) Valedictorian

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This question can be solved as follows.

On the first map the scale is 1:20000 and the area of the forest is 50 cm^2.

With a scale of 1:20000, a unit length on the map represents a length of 20000. 1 cm^2 = 1 cm* 1 cm which represents 20000*20000 cm^2 = 4*10^8 cm^2

50 cm^2 represents 4*50*10^8 cm^2 = 200* 10^8 cm^2

Now on the other map the same 200* 10^8 is represented by 8 cm^2. So the scale is sqrt [ 200* 10^8 / 8 ] = sqrt [ 25* 10^8 ] = 5* 10^4 = 50000.

Therefore the scale on the second map is 1: 50000.

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