Ten boxes are packed tightly in a crate. From above, the packed crate looks like this: [asy] size(4cm); draw((0,10)--(12,10)--(1
2,0)--(0,0)--cycle,black+3); draw((0,7)--(12,7)); draw((0,4)--(12,4)); draw((4,10)--(4,4)); draw((8,10)--(8,4)); draw((3,4)--(3,0)); draw((6,4)--(6,0)); draw((9,4)--(9,0)); label("$\ell$",(6,10),N); draw((5.3,10+.9)--(0,10+.9),EndArrow(TeXHead)); draw((6.7,10+.9)--(12,10+.9),EndArrow(TeXHead)); label("$w$",(12,5),E); draw((12.9,5.7)--(12.9,10),EndArrow(TeXHead)); draw((12.9,4.3)--(12.9,0),EndArrow(TeXHead)); [/asy] 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?
