The floor is 28 by 35 tiles wide, meaning the ratio of the sides of the

rectangle represented by the floor is 4:5.





If you had the same floor covered with rectangular tiles whose sides were in

ratio 4:5 and large enough that the floor would be completely covered by a

7 by 7 grid of these larger tiles, the string would hit each one of the larger

tiles at a corner.





Each one of these larger tiles, being in a 4:5 ratio length to width, would

cover a 4 tile by 5 tile area on the existing floor.  So all you need is a

diagram of 4 tiles by 5 tiles, draw a line from corner to corner and then

count the tiles crossed by the line.  I counted 8.  Since there are 7 of 

these 4 by 5 tile areas across the floor, the string mentioned in the problem

covers 7 times 8 or 56 tiles. 

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