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Math Help - Rectangular

  1. #1
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    Rectangular

    The rectangular WZYX is inside the rectangular ACDB

    AB= 8 cm
    AC= 6 cm
    WX= 8 cm

    What is WZ= ?

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  2. #2
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    Re: Rectangular

    There are an infinite number of possible solutions. Imagine sliding point X toward A or B. You can aways rotate line XW around X so that W stays on AC. Each angle gives a different solution.
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  3. #3
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    Re: Rectangular

    1 possible solution only:

    ax=6.2233
    aw=5.027
    wz=1.2507
    cz=0.78594
    wc=0.97296
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  4. #4
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    Re: Rectangular

    Why not (as an attempt) make angle AWX = 60 degrees; then AW = 4 and AX = 4SQRT(3)
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  5. #5
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    Re: Rectangular

    Quote Originally Posted by Mhmh96 View Post
    The rectangular WZYX is inside the rectangular ACDB

    AB= 8 cm
    AC= 6 cm
    WX= 8 cm

    What is WZ= ?
    If and only if the points W, X, Y and Z has to be placed on the sides of the rectangle ABCD and |\overline{WX}| = 8 Then there is only one unique solution of this question. See attachment #2 to see what happens if |\overline{AX}| is changing but |\overline{WX}| remains constant. Only the thick outlined quadrilateral is a rectangle, all other quadrilaterals are trapezoids.

    According to the labeling in attachment #1 you'll get:

    8^2 = (8 - x)^2 + (6 - y)^2 ........... [1]

    The adjacent sides of the rectangle are perpendicular to each other. Using the slopes of the sides you'll get:

    -\frac yx \cdot \frac{6-y}{8-x}=-1 ........... [2]

    From [2] you'll get: x = 4 - \sqrt{y^2 - 6y + 16}

    Plug in the term of x into [1] and solve for y. I've to confess that this task was done by my calculator. You'll get:

    y \approx 1.895734320 and consequently
    x \approx 1.133049932

    Since |\overline{XY}| = |\overline{WZ}| you'll get |\overline{WZ}| \approx \sqrt{1.895734320^2 + 1.133049932^2} \approx 2.208531358
    Attached Thumbnails Attached Thumbnails Rectangular-rctinrectplan.png   Rectangular-rcteckinrcteck.png  
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  8. #8
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    Re: Rectangular

    as the Hausdorff dimension which should be fractional in the case of wallets a fractal, and a major part of this is related to the self-similarity since this self-similarity creates weird dependencies in the actual information content of the object itself.louis vuitton handbags
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