   SEARCH HOME Math Central Quandaries & Queries  Question from lachlan, a student: A farmer uses a rope to tether a goat to a pole at the corner of a square paddock. The length of one side of the square is 24m. a) If the length of the rope is 12m,what % of the paddock can the goat reach? is the answer 19.62 %? b) If the farmer wants the goat to be able to graze exactly half the area of the paddock, what length must the rope be? Lachlan,

For a I got ratio of the area that the goat can graze to the area of the paddock to be π/16 which is 19.63%.

Since our answers agree in part a I expect we made the same calculation. You can use the same idea for part b. This time you don't know the length of the rope so call it r m. The region that the goat can graze is then a quarter circle of radius r. Write an expression for the area of one quarter of a circle of radius r and set it equal to one half the area of the paddock. Solve this for r.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.