Yes.
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The floor or ceiling of a rectangular 11' by 12' room.
It depends on the rectangular what.
132 is a composite number but 5 is not one of its factors
If you define a rectangular number as a number which is the product of two consecutive integers, it cannot be square.
No it isn't. 1 is an odd number and if you continue going up, e.g. 1,3,5,7,9... you would never get 132. You would get 131 and 133 but not 132. Whereas 2 is an even number and if you continue going up, e.g. 2,4,6,8,10,12, you would eventually reach 132 therefore 132 is an even number.