A spider sits at one of the corners of a rectangular box which has sides with a length of 1 metre. It badly wants to reach an ant which sits at the centre of one of the faces of the box the furthest from the spider. What is the shortest distance that the spider needs to travel along the surface in order to have its meal?

Draw a diagram of the box with the sides unfolded and lying flat. Now draw a straight line from spider to fly, and the distance x is

x^2 = (1/2)^2 + (3/2)^2

To find the shortest distance the spider needs to travel along the surface of the box to reach the ant, we need to calculate the path using the Pythagorean theorem.

Step 1: Determine the length of the diagonal of the rectangular box.
The rectangular box has sides with a length of 1 metre. Let's label the corners of the box as A, B, C, and D. We can imagine a diagonal line connecting corners A and C. The length of this diagonal can be found using the Pythagorean theorem.

Using the formula c² = a² + b², where c is the diagonal length and a and b are the lengths of the sides of the rectangle, we can calculate the diagonal length:

c² = 1² + 1²
c² = 2

Taking the square root of both sides, we find:

c = √2

So, the length of the diagonal of the rectangular box is √2 meters.

Step 2: Determine the distance from the spider to the ant.
Since the spider is at one of the corners of the box, and the ant is at the center of one of the faces furthest from the spider, the distance between them can be found by drawing a straight line from the spider to the ant.

The distance between the spider and the ant is half the length of the diagonal of the box, because the ant is at the center of the face.

Therefore, the distance between the spider and the ant is (1/2) * √2, which simplifies to √2/2 meters.

So, the shortest distance the spider needs to travel along the surface of the box to reach the ant is √2/2 meters.