The field must have contained between 179 and 180
acres—to be more
exact, 179.37254 acres.
Had the measurements been 3, 2, and 4 furlongs
respectively from successive corners, then the field would have been
209.70537 acres in area.
One method of solving this problem is as follows.
triangle APB in terms of x, the side of the square.
Divide by x and then
square, and we have the value of y2 in terms of x.
Similarly find value of z2
in terms of x;
then solve the equation y2+z2=32,
which will come out in the
square furlongs, very nearly, and as there are ten acres in one square
furlong, this equals 179.37254 acres.
If we take the negative root of
equation, we get the area of the field as 20.62746 acres, in which case
the treasure would have been buried outside
the field, as in Diagram 2.
But this solution is excluded by the condition that the treasure was
buried in the field.
The words were, "The document ... states clearly
that the field is square, and that the treasure is buried in it."