How long should the bridge across the pond be?

Question

A new bridge that is going to be built over a pond in the park so that visitors can walk across and rest on the benches on either side. There is a triangular walkway around the pond, and the benches are located halfway along the sides of the triangle. A surveyor has measured the base of the triangle to be 2,640 feet across. How long should the bridge across the pond be?

Answer 1

Draw and label a diagram of triangle ABC, with BC the base.

Mark the midpoint of AB as D, and the midpoint of AC as E. These are the location of the benches.

DE is parallel to BC and equal to one-half its length. (The triangles are similar)

The bridge should be 1320 feet.