9. what is the longest flagpole (in whole feet) that could be
shipped in a box that measures 2 ft by 2 ft by 12 ft?
12 ft

Step-by-step explanation:

If the pole lies flat on one side of the box, with one end in each of the two opposite vertices of the box, and d represents the length of the pole, then:

d² = 12² + 2², or d² = 144 + 4 = 148 ft².  d (the longest pole length) would then be 12.17 ft.

If the pole has one vertex in one of the four lower corners of the box, and if it reaches diagonally to the opposite vertex 2 feet up, then:

d² = 2² + 2² + 12², or 4 + 4 + 144 (all in ft²).  Then d = 12.33 ft.