Math Problem

Question

A rectangular floor is completely covered with tiles that measure 1 m by 2 m. If the tiles cannot be cut and do not overlap, which dimensions of the following are not those of this floor. Explain your reasoning.

(a) 4 m by 9 m    (b) 8 m by 8 m     (c) 11 m by 7 m

Answer 1

Your reasoning should follow some rational (that is, logical) sequence:

 

1.  "the tiles cannot be cut and do not overlap" means that the total area must be an integer multiple of the tile size.  That is, we ask, "Is the floor area evenly divisible by the individual tile area?"

    (a) 4 m by 9 m     Is 36 m² evenly divisible by 2 m² ?    Yes

    (b) 8 m by 8 m     Is 64 m² evenly divisible by 2 m² ?    Yes

    (c) 11 m by 7 m   Is 77 m² evenly divisible by 2 m² ?  No.  Eliminate (c).

 

2. Is there a possible pattern for laying the tiles in the floor area?

   Let each tile look like a domino (AB) for our purposes.

   (a) 4 m by 9 m

         A A A A A A A A A

         B B B B B B B B B

         A A A A A A A A A

         B B B B B B B B B

              Yes. It takes 18 tiles  (that is, 36/2).

   (b) 8 m by 8 m  

        A A A A A A A A

        B B B B B B B B

        A A A A A A A A

        B B B B B B B B

        A A A A A A A A
        B B B B B B B B
        A A A A A A A A
        B B B B B B B B

          Yes.  It takes 32 tiles (that is, 64/2).

We have shown that either (a) or (b) could be dimensions of this floor.

Answer 2

Hi Morgan,

 

The answer is C because you can not fit 1 by 2 m tiles perfectly to a 7 by 11 m space. Both dimensions even or one even and one odd would work but not when both are odd. You can think of it as finding multiples. 

Hope this helps.