SOLUTION: Five tiles, each 1 foot square, were used to cover a spot on a floor. The tiles had to be placed so that the sides of any two tiles matched evenly. The perimeter of the spot that

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Question 1134777: Five tiles, each 1 foot square, were used to cover a spot on a floor. The tiles had to be placed so that the sides of any two tiles matched evenly. The perimeter of the spot that was covered was 10 feet. What are the possible shapes for the spot?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


There is no mathematical magic to answering this. You can solve the problem yourself as easily as we can.

Draw all the different configurations you can think of for the 5 tiles and find which have a perimeter of 10 feet.
Answer by ikleyn(52806)   (Show Source): You can put this solution on YOUR website!
.

1.  Five tiles have 5*4 = 20 edges.



2.  We are given that the perimeter of the spot is 10 feet.

    It means that there are 10 edges opened to outside.


    It means, in turn, that 10 other edges are adjacent one to the other,

    so  10/2 = 5 edges are commonly (in-pairs) adjacent.



3.  These hints  helped / facilitated  me to find the spot configuration.


    Here it is :    X X
                    X X X


    Calculate the outer perimeter. There are 10 edges opened to outside,

    so this configuration (and every other equivalent to it) satisfies the condition.

Solved.


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