Starting from point X, a person walked 20 m towards South to reach point Y. From there, he took a left turn and walked 25 m to reach point Z. He then took a left turn and walked for another 20 m to reach point P. What is the approximate shortest distance between the points X and Z and in which direction is the person's final position with respect to point X?
32 m, East
In the diagram below, the minimum distance between the initial point x and point z is marked by point X and Z respectively.
Now, the triangle "XYZ" is a right-angled triangle, so using the Pythagorean theorem:
XZ2 = XY2 + YZ2
XZ2 = (20)2 + (25)2
XZ2 = 400 + 625
XZ2 = 1025
XZ2= √ 1025
XZ = 32.015
XZ is approximately equal to 32.
The final position P East in relation to point X.
Thus, the minimum distance is 32 meters, and the final direction is East relative to the initial direction.
Therefore, the correct answer is "32 meters, East".
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