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?
+36916 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)
+128460 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
