Farmer Jones and his Grazing Goat

by

Laura Singletary

Problem: Farmer Jones had a goat on a tether. He tied the end of the tether not attached to the goat to a stake in a field. Over what area could the goat graze? Of course you need to know something about the length of the tether and about the field. There are two structures in the field:

• A shed that is 20 ft long and 20 feet wide (square)

• A silo that is 20 ft in diameter The center of the shed and the center of the silo are on a line and the distance apart is 92 feet.

The tether for the goat is 76.7 feet long. The stake to which the tether is tied is somewhere along the line of centers between the shed and the silo.

Case 1: The Tether is Staked at the Barn's Door

Case 2: The Tether is Staked at the Silo's Door

Considering these two cases, you can help Farmer Jones determine where to place his tether. Would there be an even better place to ground the stake? Why? I encourage you to try other cases.