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?

Guest Oct 31, 2018

edited by
Guest
Oct 31, 2018

#1**+1 **

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)

ElectricPavlov Oct 31, 2018

#3**+2 **

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

CPhill Oct 31, 2018