THE THREE VILLAGES.
(
Money Puzzles)
I set out the other day to ride in a motor-car from Acrefield to
Butterford, but by mistake I took the road going _via_ Cheesebury, which
is nearer Acrefield than Butterford, and is twelve miles to the left of
the direct road I should have travelled. After arriving at Butterford I
found that I had gone thirty-five miles. What are the three distances
between these villages, each being a whole number of miles? I may
mention that the three roads are quite straight.
Answer:
Calling the three villages by their initial letters, it is clear that
the three roads form a triangle, A, B, C, with a perpendicular,
measuring twelve miles, dropped from C to the base A, B. This divides
our triangle into two right-angled triangles with a twelve-mile side in
common. It is then found that the distance from A to C is 15 miles, from
C to B 20 miles, and from A to B 25 (that is 9 and 16) miles. These
figures are easily proved, for the square of 12 added to the square of 9
equals the square of 15, and the square of 12 added to the square of 16
equals the square of 20.
