Algebra based question - XP Math - Forums

 XP Math - Forums Algebra based question

 12-05-2006 #1 MM92 Guest   Posts: n/a Algebra based question Hi everyone, I am new to this site. I was wondering if anyone here can help me answer a question, in order for me to study correctly for my math test tomorrow. Here's the question: Melissa plans to put a fence around her rectangular garden. She has 150 feet of fencing material to make the fence. If there is to be a 10 foot opening left for an entrance on one side of the garden, what dimensions should the garden be for maximum area? This question has to be answered in vertex form. If anyone can answer this and explain it step by step to me that would be great!
 12-06-2006 #2 zwu_ca Guest   Posts: n/a Solution: Suppose one side of the rect is x, the other side is (160-2x)/2=80-x (taking account of 10 feet of the door).. The area is x(80-x) = 80x - x^2 = 1600 - (1600-80x+x^2) = 1600 - (x-40)^2. So maximum area is reached when x is 40. The dim is 40x40. http://www.mathpotd.org
 12-06-2006 #3 MM92 Guest   Posts: n/a So that would be how u do it in vertex form? what does ^ this mean? Thanks
 12-06-2006 #4 zwu_ca Guest   Posts: n/a x^2 = x.x, i.e., x times x. The vertex form can be many, many. Here is a one: (0,0), (0,10), (0,40), (40,40), (40,0). Last edited by zwu_ca; 12-06-2006 at 06:51 PM..
 12-06-2006 #5 Cookie Dough 7 Guest   Posts: n/a wait i think i do....so the answer is 40 by 40 or do i have 2 do another step?
 12-07-2006 #6 zwu_ca Guest   Posts: n/a We don't know what exactly the original problem is. If the original problem required the vertex form, we have to do another step. Math Problem of the Day
 12-08-2006 #7 Scion   Join Date: Nov 2006 Posts: 437 what is vertex? u mean angles blah i dony know __________________
03-30-2007   #8
Scion

Join Date: Nov 2006
Posts: 437

Quote:
 Originally Posted by zwu_ca Suppose one side of the rect is x, the other side is (160-2x)/2=80-x (taking account of 10 feet of the door).. The area is x(80-x) = 80x - x^2 = 1600 - (1600-80x+x^2) = 1600 - (x-40)^2. So maximum area is reached when x is 40. The dim is 40x40. http://www.mathpotd.org
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