Question 1147968: The floor of a rectangular room is completely covered with square tiles. The room is 9 tiles long and 5 tiles wide. Find the number of tiles that touch the walls or door of the room.
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! 24
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The workout:
Along the perimeter: 2*9 + 2*5 = 28 but subtract 4 because each corner is counted twice, leaving 24.
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More generally...
To see the pattern, imagine the room has only 4 tiles in a 2x2 arrangment: the perimeter is 2*2+2*2 = 8, and subtracting 4 leaves 4.
For a 3x3 configuration: 2*3+2*3 = 12, 12-4 = 8 (clearly correct as only the center tile does not touch a wall or door, and 3*3-1 = 8).
etc.
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