Consider the following problem: A farmer has 3,600 feet of fencing and wants to fence off a rectangular field that borders a straight river. The farmer does not need a fence along the river (see the figure).

What are the dimensions of the field of largest area that can be fenced? (Letxbe the width of the field in feet andlbe the length of the field in feet.)

(a)Experiment with the problem by drawing several diagrams illustrating the situation. Calculate the area of each configuration, and use your results to estimate the dimensions of the largest possible field (in feet). (Round your answers to the nearest hundred feet.)

x= ?ft

l = ?ft

(b)Find a function that models the area of the field in terms of one of its sides.

A(x) =

(c)Use your model to solve the problem, and compare with your answer to part (a). (Enter your answers in feet).

x= ? ft

l= ?ft