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sana.noor GMAT Destroyer! Default Avatar
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help Post Fri Aug 23, 2013 11:12 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    In the figure Shown,two identical squares are inscibed in the rectangle.if the area of the rectangle is 36 Sq. Units,then what is the perimeter of each Square??



    i dont have its answer

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    Post Sat Aug 24, 2013 12:21 am
    Hi sana.noor,

    In the drawing that you provided, you should notice that:

    the width of the rectangle = 2(square's diagonal)
    the height of the rectangle = 1(square's diagonal)

    Using square "rules", the diagonal = x(root2)

    So the area of the rectangle = (width)(height) = 2(x(root2))^2 = 36

    Let's simplify:
    (x(root2))^2 = 18
    x^2(2) = 18
    x^2 = 9
    x = 3

    So the perimeter of each square = 3(4) = 12

    GMAT assassins aren't born, they're made,
    Rich

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    Post Sat Aug 24, 2013 5:36 am
    sana.noor wrote:


    In the figure shown, two identical squares are inscribed in the rectangle. If the area of the rectangle is 36, what is the perimeter of each square?

    Here's a slightly different approach:
    Since the height of the rectangle and the diagonal of a square are the same length, let's let x = height of rectangle


    Since the width of the rectangle is equal to the length of two square diagonals, then the width of the rectangle = 2x.


    The area of the rectangle is 36.
    So, (base)(height) = 36
    (2x)(x) = 36
    2x²= 36
    x²= 18
    x = √18

    NOTE: There's no need to simplify √18 at this point (you'll see why shortly)

    If the height of the rectangle is √18, then the length of the red line (shown below) must equal √18/(2)


    Likewise, the other red line has length √18/(2)


    If we let y = the length of the hypotenuse, then the Pythagorean Theorem states that...


    Now solve this equation for y.


    If y = 3, then the perimeter of one square = (4)(3) = 12

    Cheers,
    Brent

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    happy888 Just gettin' started! Default Avatar
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    Post Sun Jan 10, 2016 3:07 pm
    Hi Brent,

    I didn't understand why 1/4th length of the rectangle is squareroot18/2

    Thanks

    Post Sun Jan 10, 2016 8:33 pm
    Hi happy888,

    The 'key' to this whole question is in realizing that the width and height of the rectangle can be expressed in terms of the DIAGONAL of each of the SQUARES. Are you able to follow the 'set-up' of the calculations involved?

    GMAT assassins aren't born, they're made,
    Rich

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    Post Sun Jan 10, 2016 9:38 pm
    happy888 wrote:
    Hi Brent,

    I didn't understand why 1/4th length of the rectangle is squareroot18/2

    Thanks
    Once we know that the height of the rectangle is √18, then HALF of that is (√18)/2


    I hope that helps.

    Cheers,
    Brent

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    Brent Hanneson – Founder of GMATPrepNow.com
    Use our free video course along with Beat The GMAT's free 60-Day Study Guide

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    happy888 Just gettin' started! Default Avatar
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    Post Wed Jan 13, 2016 4:40 am
    Hi,

    Got it

    Thanks Smile

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