SOLUTION: can you help me set-up this problem a homeowner wants a fence to rectangular garden using 150 ft of fencing. the side of the garage will be used as one side of the rectangle. fi

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: can you help me set-up this problem a homeowner wants a fence to rectangular garden using 150 ft of fencing. the side of the garage will be used as one side of the rectangle. fi      Log On


   

Question 76987: can you help me set-up this problem
a homeowner wants a fence to rectangular garden using 150 ft of fencing. the side of the garage will be used as one side of the rectangle. find the dimensions for which the area is a maximum.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the 2 opposite sides x
and the side parallel to the garage 150+-+2x
Note that x+%2B+x+%2B+%28150+-+2x%29+=+150
Call the area A
A+=+x%28150+-+2x%29
A+=+-2x%5E2+%2B+150x
If the coefficient is negative, that means this
parabola has a maximum
When the form of the equation is y+=+ax%5E2+%2B+bx+%2B+c,
The maximum occurs at x+=+-b+%2F+2a
where a+=+-2, b+=+150
-b+%2F+2a+=+150+%2F+4
150+%2F+4+=+37.5
When x = 37.5 feet, the area is a maximum
check answer
Does the perimeter equal 150 feet?
x+%2B+x+%2B+%28150+-+2x%29+=+150
2%2A37.5+%2B+75+=+150
75+%2B+75+=+150
OK
Is the area a little less if I make x a little
smaller(like 37) or a little bigger (like 38)
I'lll leave this checking for you