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    • Thread Starter

    Hi just doing the 2005 jan OCR c1 paper and stuck on question 8iii

    The question reads:
    The length of a rectangular children's playground is 10m more than it's width. The width of the playground is Xm

    i) The perimeter of the playground is greater than 64m. Write down a linear inequality in X

    ii) The area of the playground is less than 299m^2. Show that (X-13)(X+23)<0

    iii) By solving the inequalities in parts i and ii, determine the set of possible values of x

    Ok so managed i and ii fine, by i being 4X + 20 > 64 and ii being proven

    Stuck on part iii though..

    Have determined x>11 by re-arranging part i but not sure how to go about the rest of it..


    Can you solve the quadratic inequality (X-13)(X+23)<0 ? Consider a sketch.
    Then combine the solution with the other one x>11.
    • Community Assistant

    Community Assistant
    Do you know how to sketch y = (x - 13)(x + 23) ?

    For what x values would y be less than 0 ?

    Don't forget that x also has to be greater than 11. Combine these pieces of information.
    • Thread Starter

    (Original post by vc94)
    Can you solve the quadratic inequality (X-13)(X+23)&lt;0 ? Consider a sketch.
    Then combine the solution with the other one x&gt;11.

    So from sketching gives the inequalities -23<x<13

    and x>11 from using part i

    So 11<x<13 !

    Thank you!
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Updated: March 28, 2011

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