Consider equilateral triangle ABC with sides of length 10.
Let point P be any point located interior to triangle ABC.

Questions to consider:
1. Find the sum of the distances from point P to each of the sides of triangle ABC.

2. How do you know you have calculated the correct sum? Can you justify your solution strategy?

3. Would your strategy work if the triangle was not equilateral (and you knew the lengths of each side)? Explain.

4. What other aspects of this problem can you explore?

Problem adapted from:
Education Development Center (2000). Connected Geometry. Chicago: Everyday Learning.