Question 1155358: A farmer has 2400 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.
(c) Use your model to solve the problem, and compare with your answer to part (a). Maximum area occurs at the following values.
which is looking for
smaller dimension:
larger dimension:
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
Answer by ikleyn(52778)  (Show Source):
You can put this solution on YOUR website! .
It is a classic problem on finding optimal dimension.
This problem was solved MANY TIMES in this forum.
Therefore, I created a lesson at this site, explaining the solution in all details.
The lesson is under this link
- A farmer planning to fence a rectangular area along the river to enclose the maximal area
Read this lesson attentively.
Consider it as your TEMPLATE.
Having this template in front of you, solve the GIVEN problem by the same way.
Having it written one time, I do not see any reasons to re-write it again and again with every new posted data set.
By the way, in the lesson, you will find many useful links to accompanied lessons.
Do not miss them.
Consider my lessons as your textbook, handbook, tutorial and (free of charge) home teacher.
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