Given that 50mm on a map represents 4km on the groun.
A.Calculate the distance in km between two villages which are represented on the map by points 75mm apart.
B.Express the scale of the map in the form 1:n
C.Calculate in mm squared the area of the map which represents a region of 48squared on the ground
50 mm ----> 4 km
1 mm ------> 4/50 km
75 mm ----> (75)(4/50) km or 6 km
ratio = 50 mm : 4 km
= 50 mm : 4000000 mm
= 1 : 80,000
c) "48squared" km?
from your given:
(4 km)^2 ---> (50 mm)^
16 km^2 = 2500 mm^2
1 km^2 = 2500/16 mm^2
48 km^2 = (48)(2500/16) mm^2 or 7500 mm^2
A. To calculate the distance in km between the two villages represented on the map by points 75mm apart, we can use the given scale of 50mm representing 4km.
We can set up a proportion to solve for the unknown distance:
50mm / 4km = 75mm / x
Cross-multiplying, we get:
50mm * x = 4km * 75mm
x = (4km * 75mm) / 50mm
Simplifying, we have:
x = (4km * 75) / 50
= 6km
Therefore, the distance between the two villages is 6 km.
B. The scale of the map can be expressed in the form 1:n, where n represents the ratio of the measurement on the map to the corresponding measurement on the ground.
Since 50mm on the map represents 4km on the ground, the ratio can be expressed as:
1 : (50mm/4km)
To simplify the ratio, we can convert 50mm to meters and 4km to meters:
1 : (50mm/4km)
= 1 : (0.05m/4000m)
= 1 : 0.0000125
Therefore, the scale of the map can be expressed as 1:0.0000125.
C. To calculate the area on the map that represents a region of 48 km² on the ground, we need to use the scale of the map.
Given that 50mm represents 4km, we can find the area on the map by squaring the ratio of the measurements:
(50mm/4km)^2 = (50mm^2)/(4km)^2 = (50mm^2)/(16km^2)
Now, we can substitute the value of 48 km² into the equation:
Area on map = (50mm^2)/(16km^2) * 48km^2
Simplifying, we get:
Area on map = (50mm^2 * 48km^2) / (16km^2)
Area on map = (50mm^2 * 48km^2) / (16km^2)
= (50 * 50 * 48) mm²
= 120,000 mm²
Therefore, the area of the map that represents a region of 48 km² on the ground is 120,000 mm².