# Rectangular

• Aug 24th 2012, 02:33 PM
Mhmh96
Rectangular
The rectangular WZYX is inside the rectangular ACDB

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

What is WZ= ?

http://store2.up-00.com/Aug12/yLN47559.jpg
• Aug 24th 2012, 02:50 PM
HallsofIvy
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.
• Aug 24th 2012, 03:31 PM
MaxJasper
Re: Rectangular
1 possible solution only:

ax=6.2233
aw=5.027
wz=1.2507
cz=0.78594
wc=0.97296
• Aug 25th 2012, 02:55 AM
Wilmer
Re: Rectangular
Why not (as an attempt) make angle AWX = 60 degrees; then AW = 4 and AX = 4SQRT(3)
• Aug 25th 2012, 10:39 AM
earboth
Re: Rectangular
Quote:

Originally Posted by Mhmh96
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: $x = 4 - \sqrt{y^2 - 6·y + 16}$

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 $|\overline{WZ}| \approx \sqrt{1.895734320^2 + 1.133049932^2} \approx 2.208531358$
• Nov 1st 2012, 01:48 AM
elisaevedent
Re: Rectangular
• Nov 8th 2012, 07:21 PM
Chalama123
Re: Rectangular
• Nov 18th 2012, 11:35 PM
jesong
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