the distance between two towns A and B is 150 kilometers. This distance is represented on a map by a length of 300 millimeters. If the scale of this map is in the form of 1:a, find the value of a
.3 meters represent 150,000 meters
1:500,000
To find the value of "a" in the scale of the map, we can use the ratio between the distance on the map and the actual distance.
Here's how you can calculate it:
1. Determine the scale on the map. In this case, the scale is given as 1:a, where "a" is the value we're trying to find.
2. Measure the length of the distance between towns A and B on the map. In this case, it is 300 millimeters.
3. Measure the actual distance between towns A and B. In this case, it is given as 150 kilometers.
4. Set up a proportion using the distance on the map and the actual distance:
distance on map / actual distance = map scale / scale value
In this case, we have:
300 mm / 150 km = 1 / a
5. Convert the actual distance to the same unit as the distance on the map. Since 1 kilometer is equal to 1,000 meters and 1 meter is equal to 1,000 millimeters, we can convert kilometers to millimeters.
150 km = 150,000 meters = 150,000,000 millimeters
6. Substitute the values into the proportion:
300 mm / 150,000,000 mm = 1 / a
7. Simplify the proportion:
300 / 150,000,000 = 1 / a
8. Solve for "a" by cross-multiplying:
300a = 150,000,000
9. Divide both sides of the equation by 300:
a = 150,000,000 / 300
10. Simplify the division:
a = 500,000
Therefore, the value of "a" in the scale of the map is 500,000.