Results 1 to 5 of 5

Math Help - Presumabley a Quadratic word problem

  1. #1
    Member
    Joined
    Oct 2009
    From
    Detroit
    Posts
    158
    Thanks
    5

    Presumabley a Quadratic word problem

    A rectangular field adjacent to a river must be fenced on 3 sides but not on the river bank. What is the largest area that can be enclosed if 50 yards of fencing is used?

    The chapter is on Quadratic Functions; Graphing them using intercepts and turning points specifically. Given this I assume that the question wants me to place it into a x^2 format.

    First off I can't figure out how to set it up as a quadratic. Secondly the best result I can get is when the sides are equal, or 50/3, which is approximately equal to 277. The answer is 312.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by bkbowser View Post
    A rectangular field adjacent to a river must be fenced on 3 sides but not on the river bank. What is the largest area that can be enclosed if 50 yards of fencing is used?

    The chapter is on Quadratic Functions; Graphing them using intercepts and turning points specifically. Given this I assume that the question wants me to place it into a x^2 format.

    First off I can't figure out how to set it up as a quadratic. Secondly the best result I can get is when the sides are equal, or 50/3, which is approximately equal to 277. The answer is 312.
    Since the pen is next to a river we only need fence on 3 sides.

    Let the side parallel to the river be l and the side perpendicular to the river be w.

    Then using the area and perimeter formula for a rectangle we get

    P=l+2w \iff 50=l+2w

    A=lw

    Now you can use the first equation to eliminate a variable from the 2nd then find the maximum of the resulting quadratic.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Start by saying the 50 yards is equal to the sum of the two sides perpendicular (x) and the side that is parallel to the river (y)

    You get x+x+y=50 or 2x+y = 50

    Now the area is just lenth times width or x times y. So in the above equation solve for y, so area can be a function of just x.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Oct 2009
    From
    Detroit
    Posts
    158
    Thanks
    5
    Ah so it should be something like x(50-2x).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Yep A =x(50-2x)

    Now where has this value a maximum? Or where is the turning point

    Hint: Half way between the zeros.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. I need help with quadratic word problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 30th 2009, 11:09 PM
  2. Quadratic Word Problem Help
    Posted in the Algebra Forum
    Replies: 7
    Last Post: March 28th 2009, 10:38 AM
  3. Quadratic word problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 9th 2009, 07:35 PM
  4. quadratic word problem
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 14th 2008, 06:13 AM
  5. Quadratic Word Problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: June 8th 2006, 03:01 PM

Search Tags


/mathhelpforum @mathhelpforum