# Setting up equations for length and width

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• Nov 7th 2012, 04:27 AM
skweres1
Setting up equations for length and width
A farmer with 500 ft. of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. He has decided that the best possible area for the field is 20,000 square feet, and the best possible layout is to have the longer side parallel to the river. What are the dimensions of the field that will result in this area?

Please Help!!!
• Nov 7th 2012, 04:47 AM
HallsofIvy
Re: Setting up equations for length and width
Do you know how to find the area of a rectangle? Suppose we call the length of the fence parallel to the river "x" and the length of fence perpendicular to the river "y". What is the formula for the area of the rectangle. What amount of fencing will he need for the two sides of the rectangle parallel to the river? How much for the one side parallel to the river? You can use the fact that he has 500 feet of fencing available to write "x" in terms of "y" (or vice-versa) so that the are depends only on one variable.