Final answer:
On a map with a scale ratio of 1:350, an actual distance of 200 meters is represented as approximately 0.5714 centimeters. A proportion is used to calculate this distance by setting up the equation 1 map unit / 350 real meters = X map units / 200 real meters and solving for X.
Step-by-step explanation:
When a map has a scale ratio of 1:350, it means that every unit of measurement on the map represents 350 units of the same measurement in the actual distance. If you want to show an actual distance of 200 meters on this map, you need to calculate the map distance using the given scale ratio.
Here's the step-by-step explanation for this calculation:
- First, set up a proportion based on the scale ratio. Since 1 unit on the map equals 350 units in reality, we have: 1 map unit / 350 real meters.
- Next, we want to find out how many map units equal the actual distance of 200 meters. So, we set that as our proportion: map units (unknown) / 200 real meters.
- Now we can set up our equation like this: 1 map unit / 350 real meters = X map units / 200 real meters.
- To solve for X, we cross multiply: (1 map unit * 200 real meters) = (X map units * 350 real meters).
- After doing the multiplication, we get: 200 = 350X.
- Now, divide both sides by 350 to solve for X: 200 / 350 = X.
- X ≈ 0.5714 map units.
- Since most maps use centimeters as the unit, we'll convert this to centimeters. Therefore, the actual distance of 200 meters will be shown as approximately 0.5714 cm on the map.
So, on the map with a scale ratio of 1:350, the 200-meter actual distance would be represented as approximately 0.5714 centimeters.