Let AP and BQ be two vertical poles at points A and B, respectively. If `A P = 16 m , B Q = 22 m a n d A B = 20 m`, then find the distance of a point R on AB from the point A such that `R P^2+R Q^2`is minimum.

Explanation

To solve the problem, we need to find the distance of point R on line segment AB from point A such that the sum \( RP^2 + RQ^2 \) is minimized.

### Step-by-Step Solution:

1. **Define the Variables:**
- Let \( AP = 16 \, m \) (height of pole at A)
- Let \( BQ = 22 \, m \) (height of pole at B)
- Let \( AB = 20 \, m \) (distance between the two poles)
...