Final answer:
The trees are 12.5 centimeters apart on the garden plan with a scale of 1:200 after converting the actual distance of 25 meters into plan units using the scale factor.
Step-by-step explanation:
To determine how far apart the trees are on the garden plan with a scale of 1:200, you start by setting up a ratio that compares the scale distance on the plan to the actual distance in reality. Since we know the actual distance between two trees is 25 meters and the scale is 1:200, for every 1 unit on the plan, there are 200 units in real life.
Now, we set up the proportion as follows:
1 unit (on plan) / 200 units (real life) = X units (on plan) / 25 meters (real life)
We solve for X, which represents the distance on the plan:
X = (1 unit / 200 units) * 25 meters
X = 25/200
X = 0.125 meters
However, plans are typically measured in centimeters, so we convert meters to centimeters:
X = 0.125 meters * 100 centimeters/meter = 12.5 centimeters
Therefore, on the plan, the trees would be 12.5 centimeters apart.