British flag theorem

The British Flag Theorem is a way of figuring out the distance between opposite corners of a rectangle. Imagine a rectangular flag, like the ones flown in Britain. If we draw a diagonal line from one corner of the flag to the opposite corner, we can use the British Flag Theorem to calculate the length of that line.

The first step is to label the length and width of the rectangle. Let's say the length is 3 and the width is 2. We can draw a square around the rectangle that shares the same center point. This square has a side length of 3 + 2 = 5.

Now we can draw two diagonal lines inside the square. These lines intersect at the center of the square and divide it into four equal triangles. One of these triangles covers half of the rectangle.

To use the British Flag Theorem, we need to find the area of both the rectangle and the two triangles that cover it. The area of the rectangle is (3 x 2) = 6. The area of one of the triangles is (3 x 2 / 2) = 3.

So we have the area of the rectangle and the area of the two triangles that cover it. Now we just need to add them up and take the square root. (6 + 2 x 3) = 12. The square root of 12 is approximately 3.46.

That means the diagonal distance between the two opposite corners of the rectangle is about 3.46! The British Flag Theorem is a neat way to use geometry to solve a problem like this.