The maximum dimension of the shelf is given by the space diagonal
length of the shelf.
A possible reason why the shelf hits the ceiling is because the ceiling is
less than or equal to 9 feet from the ground.
Reasons:
The maximum height of the shelf is given as follows;
The diagonal of one of the side = √(8² + 4²)
The diagonal of the completed shelve = √((√(8² + 4²))² + 1²) = 9
The maximum extension of the shelve = 9 feet
Given that the shelf touches the ceiling, we have, that maximum height of
the ceiling = 9 feet.
Therefore, the shelf touches the ceiling because, height from the floor to
the ceiling is lesser than equal to 9 feet.
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