Reply To: What are brains for??

Bezalel, you need brains for that? Just take out a paper and pen and do the math:

If you line up four rectangles into a box you will be left with a square space in the middle. So to get the length of a hypotenuse of one of the rectangles, you’d have to get the total area created by the four hypotenuses and get its root. That is done by doubling the area of a rectangle: 2*a*b, and adding the middle box to it: (2*a*b) + (b-a)^2. The width/height of the middle box is b-a.

Now, we have altogether: 2ab + (b-a)^2, which can be written as:

ab, ab, (b-a)*(b-a)

Using FOIL, we write out the last part as: b^2, -ab, -ab, a^2

With the two negative ‘ab’s we cancel the ab,ab and we’re left with b^2 and a^2, so who would need brains for that?