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Ten boxes are packed tightly in a crate. From above, the packed crate looks like this: https://latex.artofproblemsolving.com/miscpdf/lbqzeekw.pdf?t=1541015022365

The visible faces of the boxes are all congruent rectangles (that means the ten small rectangles in the diagram are the same shape and size). The top of the crate is \(\ell\) inches long by \(w\) inches wide, where \(\ell\ge w\) (as shown above). What is the ratio \(\ell:w\) in simplified form?

 Oct 31, 2018
edited by Guest  Oct 31, 2018
 #1
avatar+19811 
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correct ...I am incorrect

 

For the SMALL boxes    3L = 4W      (3/2 L = 2W )

 

The LARGE CRATE   is     3L /  (2W + L)   = 3L/(3/2L+L) = 3L /( 5/2*L) =  6/5   (as Chris found)

 Oct 31, 2018
edited by Guest  Oct 31, 2018
edited by Guest  Oct 31, 2018
edited by ElectricPavlov  Oct 31, 2018
 #2
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sorry but thats wrong

Guest Oct 31, 2018
 #3
avatar+104804 
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Let  x  be the width  of  one of the rectangles and let y be its height

 

From the drawing,  it appears that  4x  = 3y  ⇒   (4/3)x  = y

 

So......L  =  3y  =  3(4/3)x  =  4x

 

And  W  = y + 2x   =  (4/3)x + 2x  =  (10/3)x

 

So

 

L : W   =    4x : 10/3 x   =   4 : 10/3   =   12 : 10   =  6 : 5

 

 

cool cool cool

 Oct 31, 2018
 #4
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the answer is oh hi mark........................................................................................................................................................................................

 Oct 31, 2018
 #5
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I am friends with sssniperwolf #jointhewolfpack

 Oct 31, 2018

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