R walks a long distance every Sunday. He walks 2 km towards the north from his house and then turns right; he walks another 2 km and again turns right; next he walks 5 km and turns left; he further walks 2 km and stops. He rests for some time and returns home following a straight route without any turning point. What is the distance R walks after he has rested ?

To determine the distance R walks after resting, we trace his path on a coordinate system starting from his house at (0,0):

• Step 1: Walks 2 km North to (0, 2).
• Step 2: Turns right (East) and walks 2 km to (2, 2).
• Step 3: Turns right (South) and walks 5 km to (2, 2 - 5) = (2, -3).
• Step 4: Turns left (facing East) and walks 2 km to (2 + 2, -3) = (4, -3).

R stops at point (4, -3). He then returns home (0, 0) via a straight route. The distance of this straight return path is calculated using the Pythagorean theorem:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Distance = √((4 - 0)² + (-3 - 0)²) = √(4² + (-3)²) = √(16 + 9) = √25 = 5 km.