Question

On a map of scale 1:20000 the area of a forest is 50cm^2.On another map the area of the forest is 8cm^2.Find the scale of the second map.

Answer 1

The answer is 1: 50000... If you look down here↓:

Explanation:

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

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

Now, on the other hand, the map has 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.