EXAMPLE 3.7.2

The diagram below shows the rectangular pen in which Gomer confines his wolverines and badgers. In order to prevent the wolverines from dating the badgers, Gomer is going to build a fence running from one corner of the pen to the opposite corner, thus dividing the pen into two smaller pens. Assuming that construction of such a fence will cost $1.25 per foot, find the total cost of this fence.

Solution

We need to find the length of the fence (in feet) and multiply the length by the cost factor of $1.25 per foot.

We can use the Pythagorean Theorem to find the length of the fence, since the fence is the hypotenuse of a right triangle whose legs measure 40 yards and 20 yards respectively. Since we want the length in feet, rather than yards, we will convert those measurements to feet before using the Pythagorean Theorem.

(40 yards)(3 feet per yard) = 120 feet.

(20 yards)(3 feet per yard) = 60 feet.

Now let L be the length of the fence. According to the Pythagorean Theorem:

The length of the fence is roughly 134 feet, and the cost is $1.25 per foot, so the total cost is

($134)($1.25) = $167.50