Results 1 to 2 of 2

Math Help - HELP with INEQUALITIES

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    40

    HELP with INEQUALITIES

    I'm having issues figuring out an equation to figure this out...any help would be greatly appreciated!

    Applications The perimeter of a rectangle is to be between 170 and 230 inches. Find the range of values for its length when its width is 45 inches.

    < length <

    Applications The perimeter of a square is to be from 45 meters to 90 meters. Find the range of values for its area.

    < area <
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,546
    Thanks
    539
    Hello, epetrik!

    The perimeter of a rectangle is to be between 170 and 230 inches.
    Find the range of values for its length when its width is 45 inches.

    We know that: . P \:=\:2L + 2W

    Since W = 45, we have: . P \:=\:2L + 90

    The perimeter is between 170 and 230 inches.

    . . \begin{array}{cccccc}<br />
\text{So we have:} & 170 & < & 2L + 90 & <& 230 \\ \\[-3mm]<br />
\text{Subtract 90:} & 80 &<& 2L &<& 140 \\ \\[-3mm]<br />
\text{Divide by 2:} & 40 &<& L &<& 70 \end{array}

    Therefore, the length L must be between 40 and 70 inches.




    The perimeter of a square is to be from 45 meters to 90 meters.
    Find the range of values for its area.

    Let x = side of the square.
    The perimeter of a square is: . 4x

    The perimeter is between 45 and 90: . 45 \;<\;4x \;<\;90

    Divide by 4: . \frac{45}{4} \;<\:x\;<\;\frac{45}{2}

    The length of the side is between 11 and 22 meters.


    The area of the square is: . x^2

    So we have: . \left(\frac{45}{4}\right)^2 \;<\;x^2 \;<\:\left(\frac{45}{2}\right)^2


    Therefore: . \frac{2025}{16} \;<\;\text{Area} \;<\;\frac{2025}{4}

    The area is between: . 126\frac{9}{16}\,\text{ and }\,506\frac{1}{4}\text{ square meters.}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. inequalities
    Posted in the Algebra Forum
    Replies: 7
    Last Post: August 20th 2011, 04:56 AM
  2. inequalities
    Posted in the Algebra Forum
    Replies: 0
    Last Post: March 20th 2011, 02:42 AM
  3. Inequalities
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: July 1st 2009, 04:35 AM
  4. Inequalities
    Posted in the Algebra Forum
    Replies: 4
    Last Post: June 15th 2009, 11:26 AM
  5. inequalities
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 14th 2008, 09:57 PM

Search Tags


/mathhelpforum @mathhelpforum