Homework Help Forum: Calculus

Posted by Salman on Friday, November 6, 2009 at 8:19am.

A rancher wants to fence in an area of 500000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side. What is the shortest length of fence that the rancher can use?

• Calculus - Reiny, Friday, November 6, 2009 at 8:41am

  I will set it up for you. Let the length of the rectangle be y feet let its width be x feet. The divider will then be x feet So the length L = 3x + 2y but you know that xy = 500000 and y = 500000/x then L = 3x + 2(500000/x) differentiate, set that equal to zero and solve for x Put x back into L = ... and you are done

  
  

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