Question

In the given real-world scenario where three highways connect the centers of three towns to form a triangle, and a cell phone company wants to place a new cell tower equidistant from the centers of the three towns, how can the company determine the optimal tower location?

A. The company should place the tower randomly within the triangle formed by the towns.

B. The company should place the tower at the centroid of the triangle.

C. The company should place the tower at one of the vertices of the triangle.

D. The company should place the tower at the midpoint of one of the highways connecting the towns.

Answer 1

The cell phone company should place the tower at the centroid of the triangle formed by the three towns, as this location is equidistant from the towns' centers.

Step-by-step explanation:

To determine the optimal location for a new cell tower equidistant from the centers of three towns that form a triangle, the cell phone company should consider option B: placing the tower at the centroid of the triangle. This location is the point where the three medians of the triangle (each median being a line from a vertex to the midpoint of the opposite side) intersect, and it is equidistant from all three vertices of the triangle. The centroid is the balance point or center of mass of the triangle, making it the optimal position for equal distribution of the cell tower's signal to all three towns.