Results 1 to 3 of 3

Math Help - Quadratics Problem

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    21

    Quadratics Problem

    A 30 cm piece of wire is cut into two. One piece is bent into the shape of a square, the other piece into the shape of a rectangle with a length-to-width ratio of 2:1. What are the lengths of the two pieces if the sum of the areas of the square and rectangle is a minimum?

    This is what I did so far:

    Let x represent the width of the rectangle
    " y " square
    " z " sum of the areas

    30=2x+2x+x+x+4y
    =6x+4y
    7.5=y+1.5x
    y=7.5-1.5x

    z=y^2+2x^2
    =(7.5-1.5x)^2+2x^2
    =4.25x^2-22.5x+56.25

    but then when I try finding the vertex, by completing the square, I don't get an integer. I'm not sure what to do.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member SuperCalculus's Avatar
    Joined
    Feb 2010
    Posts
    34
    Quote Originally Posted by DemonX01 View Post
    A 30 cm piece of wire is cut into two. One piece is bent into the shape of a square, the other piece into the shape of a rectangle with a length-to-width ratio of 2:1. What are the lengths of the two pieces if the sum of the areas of the square and rectangle is a minimum?

    This is what I did so far:

    Let x represent the width of the rectangle
    " y " square
    " z " sum of the areas

    30=2x+2x+x+x+4y
    =6x+4y
    7.5=y+1.5x
    y=7.5-1.5x

    z=y^2+2x^2
    =(7.5-1.5x)^2+2x^2
    =4.25x^2-22.5x+56.25

    but then when I try finding the vertex, by completing the square, I don't get an integer. I'm not sure what to do.
    Providing your calculations to this point are correct, you need to differentiate, so this should really be in the calculus forum, but oh well.

    \frac{dy}{dx} = 9.5x - 22.5

    To find the coordinate of the stationary point, you equate \frac{dy}{dx} = 0

    So, 9.5x - 22.5 = 0

    x = 2.368421053

    Plug back in the equation to find z. I've got to go now, so I can't do it, but that's how I'd do it.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2010
    Posts
    21
    I've already considered diffrentiating, but it doesn't produce an interger, so something in my calculations is probably off. I just need to know what.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 12
    Last Post: July 18th 2011, 06:10 AM
  2. Problem solving with Quadratics x2
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 16th 2010, 10:31 PM
  3. Problem solving with Quadratics
    Posted in the Math Topics Forum
    Replies: 5
    Last Post: February 13th 2010, 04:19 AM
  4. Problem Solving with Quadratics
    Posted in the Algebra Forum
    Replies: 6
    Last Post: September 13th 2009, 07:21 AM
  5. word problem - quadratics
    Posted in the Math Topics Forum
    Replies: 6
    Last Post: July 13th 2008, 11:45 AM

Search Tags


/mathhelpforum @mathhelpforum