The math puzzle in my diary last week generated a vast email bag. Two

common confusions:

—A lot of readers did not understand “the height drawn from the right

angle to the hypoteneuse is 6 inches.” Now, I’ll allow that alternate ways

of saying this (“a perpendicular dropped from,” “the altitude…”) might be

better, and perhaps I ought to have polished Boris’s English a bit. Still,

the problem as stated seems perfectly un-ambiguous to me. I have never seen

a line drawn from a point to another line and meeting it an a non-right

angle described as a “height.” On that basis, my head is currently at

height one hundred miles above the ground. (I am sitting at my desk.)

—A lot of other (and many of the same) readers seem to believe that a

right-angle triangle with hypoteneuse 10 must have sides 6 and 8. This is

not so, as a moment’s reflection will convince you. There is in fact an

infinity of such triangles — the isosceles one, for example, with equal

sides 10/sqr(2).

—A scattering of readers thought the whole problem was invalid because

they didn’t like the (CORRECT!) way I spelled “hypoteneuse.” Ptui, I spit.

Here is my solution.