SOLUTION: A string is stretched corner to corer on a floor tiled with square tiles. If the floor is 28 tiles long and 35 tiles wide, over how many tiles does the string cover?

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.