45 . D
Sketch a diagram:
Now, where to put P so that it’s twice as far from A as from B. One
possibility is two-thirds of the way from A to B, that is, at 4:
But that’s not the only possibility. There’s also the point that’s the same
distance to the right of B as B is from A, that is, at 12:
46 . B
You’re looking for sets of three positive integers with a product of 32. The
easiest way to do that is just to list them systematically. If the smallest
dimension is 1, then the product of the other two dimensions is 32, so
there are these possibilities that include an edge of 1:
If the smallest dimension is 2, then the product of the other two
dimensions is 16, so there are these additional possibilities:
