From my house I walked 5 km towards North, I turned right and walked 3 km. Again I went one km to the South. How far am I from my house?

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².

Step 1: First, you walked 5 km north. This is the first side of the triangle.

Step 2: Then, you turned right and walked 3 km. This forms the second side of the triangle.

Step 3: You then walked 1 km south. This doesn't affect the distance between your house and your current location because you're still on the same line (the 3 km line you walked), just 1 km closer to the starting point.

So, we have a right triangle where one side is 5 km and the other side is 2 km (3 km - 1 km).

Step 4: Apply the Pythagorean theorem: a² + b² = c². In this case, a = 5 km, b = 2 km. So, c² = 5² + 2² = 25 + 4 = 29.

Step 5: To find c (the distance from your house), we take the square root of 29, which is approximately 5.39 km.

So, you are approximately 5.39 km away from your house.