[Illustration]
This problem is quite simple if properly attacked. Let us suppose the
triangle ABC to represent our half-acre field, and the shaded portion to
be the quarter-acre over which the goat will graze when tethered to the
corner C. Now, as six equal equilateral triangles placed together will
form a regular hexagon, as shown, it is evident that the shaded pasture
is just one-sixth of the complete area of a circle. Therefore all we
require is the radius (CD) of a circle containing six quarter-acres or
1½ acres, which is equal to 9,408,960 square inches. As we only want
our answer "to the nearest inch," it is sufficiently exact for our
purpose if we assume that as 1 is to 3.1416, so is the diameter of a
circle to its circumference. If, therefore, we divide the last number I
gave by 3.1416, and extract the square root, we find that 1,731 inches,
or 48 yards 3 inches, is the required length of the tether "to the
nearest inch."