(Solved): A farmer has \( 2400 \mathrm{ft} \) of fencing and wants to fence off a rectangular field that bord ...

A farmer has \( 2400 \mathrm{ft} \) of fencing and wants to fence off a rectangular field that borders a straight river. He does not need a fence along the river (see the figure). What are the dimensions of the field of largest area that he can fence? (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. (Enter your answers as a comma-separated list.) (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), Maximum area occurs at the following values. smaller dimension larger dimension