abcdefghijklmnopqrstuvwxyz
00000000011111111112222222
12345678901234567890123456
The missing word is TOY - these are three-letter words whose letters, interpreted as side lengths of a triangle, give the triangle an integral area.
Thanks to you and Denis!
Kenny Young
Ed,
Replace each letter by its place in the alphabet, thus yielding 3 integers.
Make a triangle with these integers as the lengths of the sides. Then at
least one altitude of the triangle is of integer length.
ELM 5 12 13
OIL 15 9 12
In each of the above cases, the triangle is right-angled, so any side other
than the hypotenuse is an altitude.
FEE 6 5 5 The altitude perpendicular to the side of length 6 has length 4.
GOT 7 15 20 The altitude perpendicular to the side of length 7 has length
12.
MOD 13 15 4 The altitude perpendicular to the side of length 4 has length
12.
TUM 20 21 13 The altitude perpendicular to the side of length 21 has length
12.
Aha. Each triangle has an altitude of length 12, except FEE, whose _area_
is 12.
As for the seventh word... Any anagram of a word wth this property has this
property, so DOM and TOG would do.
Richard Sabey