Quote:
Originally Posted by ceptimus
Again, Pan wins the prize for the first correct answer!
This one was easier (I think) than the last one, but I found it oddly satisfying. The 60 in the answer, one might expect  it is, after all, 3 x 4 x 5  but I would never have guessed the 37.

Dimensional analysis can work here.
If you figure 3 * 4 * 5 has to be in there, this has units of [length]
3. If you want to go to a single [length], you have to divide by [length]
2.
One side of the square coincides with the hypothenuse of the triangle, so the 5 warrants special treatment here. To get a [length]
2, one might try 3*5 + 4*5 (=35, not quite right) or 3*4 + 5*5 (=37, the right answer).
Of course, this is handwaving after the fact, but the number 37 does not just pop out of nowhere.