My Math Forum area and perimeter

 Algebra Pre-Algebra and Basic Algebra Math Forum

 February 28th, 2012, 10:42 PM #1 Senior Member   Joined: Feb 2012 Posts: 110 Thanks: 0 area and perimeter The owner of a store wants to construct a fence to enclose an outdoor storage area adjacent to the store, using all of the store as part of one side of the area. Find the dimensions that will enclose the largest area if 240 feet of fencing material are used Can you please show me how to figure this out? How do I find area? Thank you so much for your help
 February 28th, 2012, 10:58 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs Re: area and perimeter The fence will make up 3 sides of the rectangle. Let x be the two sides of the rectangle made up of fencing and y be the two sides of the rectangle where one side is fence and one side is the store. x and y are measured in feet. So we have: $2x+y=240\:\therefore\:y=240-2x=2(120-x)$ The area A of the fenced in area is: $A=xy=2x(120-x)=240x-2x^2$ Now to find the dimensions that maximize the area, we may use the axis of symmetry of the parabolic area function to do so. A parabola $ax^2+bx+c$ has the axis of symmetry: $x=-\frac{b}{2a}$ so observing for our area function we have: $a=-2,\,b=240$ and hence: $x=-\frac{240}{2(-2)}=60$ and so $y=240-2(60)=120$.

 Tags area, perimeter

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Albert.Teng Algebra 5 July 27th, 2012 07:25 AM Chee Calculus 1 April 1st, 2012 04:47 PM frankiee Algebra 7 February 6th, 2010 07:39 PM dobb7823 Algebra 11 November 13th, 2009 10:59 PM Imaxium Elementary Math 1 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top