Plank in a corridor

A straight wooden plank that doesn't bend at all is carried in a long that is 10 feet wide and seven feet high. At one point there is a T-crossing to a side passage five feet wide. How long can the plank be if it makes it through the crossing?

Originally posted by talzamir
A straight wooden plank that doesn't bend at all is carried in a long that is 10 feet wide and seven feet high. At one point there is a T-crossing to a side passage five feet wide. How long can the plank be if it makes it through the crossing?

Looks like 2 triangles 10x5 with the board being the length of the hypotenuse times two, or the square root of 125 times two= 22 feet and change. That would be if the board was carried in two dimensional space. I think the third dimension of 7 feet high, btw, the 5 foot wide corridor had an unspecified height so going by the exact wording, you can't strictly use the height so would have to treat it as a two dimensional passage.

Ah, sorry. This makes three variants:

a. The side corridor is as high as the main corridor.
b. The side corridor is extremely high.
c. The side corridor has a generic height h that will remain as a parameter to the plank length.

a. is as I had at first intended it but the others can be interesting too.