A map bearing the scale 1cm equals to 10km is reduced by four times of its area. What is the representative fraction of the new enlarged map?
Answers
Map Scale = 1 cm : 10 km
Map Scale = (1 cm)² : (10 km)²
Map Scale = 1 cm² : 100 km²
The scale of the area is reduced 4 times:
Map Scale = 1 cm² : 100 km²
New Map Scale = 1 cm² : (100 ÷ 4) km²
New Map Scale = 1 cm² : 25 km²
Find the new scale:
New Map Scale = 1 cm² : 25 km²
New Map Scale = √1 cm : √25 km
New Map Scale = 1 cm : 5 km
New Map Scale = 1 cm : 500000 cm
Answer: The representative fraction of the new enlarged map is 1/500000
Solve it logically...
Consider, for a certain map
Initial scale = 1cm implies 10km
Representative fraction = 1cm/10km = 10^-6
Area is reduced by 4 times
Assuming the map is square length will be reduced 2 times. So less space will be available.
Hence on new scale, 1cm will show double i.e. 20km
Now
1cm will imply 2×10km = 20km
Representative fraction = 1cm/20km = 5×10^-7
On new map 1cm indicates 20km.
The representative fraction of the new enlarged map is 5×10^-7.
Hope you got your answer.