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.

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.