5) In an old manor house two 3 ft wide hallways meet at right angles as shown in the figure. They both have 7.5 foot high ceilings. To the nearest foot what is the longest ladder you can get through the hallway?
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- If the ladder remains horizontal, it must fit through the corner as shown by the figure to the right.
- The length that will pass horizontally (H) is by pythagorean theorem
  H = _____ feet.
- The hall is 7.5 feet high, so we can fit it diagonally through the corner (one end on the floor, the other touching the ceiling) , by pythagorean theorem:
  L (the ladder length) =
- The longest ladder that can pass the corner is _____ feet long.
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