Question

A man walks 5 km distance straight from a place X and reaches another place Y in the western direction. At Y, he turns 90 degrees and walks straight towards North to reach the Place Z which is 12 km from Y. The distance between X and Z is

• A. 14 km
• B. 17 km
• C. 13 km
• D. 16 km

Hint:

Whenever movement is in two perpendicular directions (like north and west), use the Pythagorean theorem to find the shortest (straight-line) distance.

Answer 1

The Correct Option is C

Step 1: Draw a right-angled triangle
From X to Y = 5 km (westward), and
From Y to Z = 12 km (northward), forming a right angle at point Y.
We want the distance between X and Z, which is the hypotenuse.
Step 2: Use the Pythagorean Theorem
Let distance XZ be \( d \):
\[ d = \sqrt{(XY)^2 + (YZ)^2} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \] So, the distance between X and Z is \(\boxed{13 \text{ km}}\)