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A square field is to be fenced on two consecutive sides and along the diagonal, connecting the ends of the two sides.  Each side of the field measures 120 yards.  The fencing is sold in 1/4 mile spools (1mile=5280 feet).  How many spools must be purchased?

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We are starting with a square, which means all four of the sides of equal in length.  We are told that each side of the field is 120 yards.  Since there are 3 feet in 1 yard, this is equal to 120/3=40 feet.  The field is a square so we know that the two consecutive sides are joined by a right triangle.  We know the length of the two sides of the right triangle (40 feet each), so we can use the Pythagorean Theorem to find the hypotenuse (the diagonal of the field that is to be fenced).

40^2 + 40^2 = c^2

1600 + 1600 = c^2

c^2 = 3200

c = 56.57 feet

So the total length of fencing needed in feet is 40+40+56.57=136.57 feet.  Let's convert this number to miles.

136.57 feet * (1 mile/5280 feet) = 0.0259 miles

The fencing is sold in one quarter mile spools.  Since one quarter of a mile is 0.25 miles and we only need 0.0259 miles of fencing, one spool will be more than enough for the job.

The final answer is 1 spool.

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