challenge anyone?

[snakeeyes1000]

for info go here. Not many people replied, but I know someone will step forward and prove their prowess

http://209.120.143.185/showthread.php?threadid=184337

[Gandalf_Grey_]

ok i think i got it and here is my proof.

W = the width of the big rectangle
L = the length of the big rectangle

A = the length of the smaller rectangles
B = the width of the smaller rectangles

A = 108 = WL

AB = 108 / 3
AB = 36

A = WL = 108 = A * (A + B) = 108 = (A ^ 2) + AB = 108
AB = 36

W = (A^2) + 36 = 108
A ^ 2 = 72

A = +/- sqrt(72)

AB = 36
+/- sqrt(72) * B = 36

_________________
B = 36 / +/- sqrt(72)
A = +/- sqrt(72)

Final Answer = A + B

First Answer = sqrt(72) + (36/sqrt(72))

--->108 / sqrt(72)

there is another answer because A is actually +/- sqrt(72) and B is actually 36 /(+/- sqrt(72)) however that leaves 2 answeres one where the area is negative and once where the area is posotive. The negative one can be discarded leaveing the posotive one

My favorite language is C++, with PHP coming in a close second

[snakeeyes1000]

I'm sorry, I can't see where you made the mistake, but that's not it. I admire your effort though. One mistake is at the end, you failed to simplify

sqr(72)
to
6*sqr(2).

[markman]

sqrt(72) + (36/sqrt(72))

is another way of putting what stevecrm had, just not simplified

[snakeeyes1000]

the question asks for simplest form. I don't give charity when it comes to tests of wit.

[Gandalf_Grey_]

even though it is wrong you can still simplify it further to 18/sqrt(2)

I will check my answer again to see where i made the error

[Gandalf_Grey_]

how about 3(sqrt(18))

[Gandalf_Grey_]

or 9 * sqrt(2)

[Guv]

There is a very simple analysis.

The small rectangles must have a length which is twice the width, and an area of 36 (108/3).

Hence 2x*x = 36, or x² = 18

If x² = 18, then x = 3*Sqr(2)

Small rectangle is 3*Sqr(2) by 6*sqr(2), and sum is 9*Sqr(2)

[bugzpodder]

9*sqrt(2), exactly how Guv got it.