A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles. A possible value of the number of tiles
along one edge of the floor is
A. 10
B. 12
C. 14
D. 16

• 12 tiles.
  
  size of room is 12x5 units and tiles are 1x1 unit.
  Total 60 tiles are used.
  out of which 30 tiles are red which are used in (12-2)*(5-2) = 10*3 unit area.
• 12 years agoHelpfull: Yes(4) No(6)
• let no of tiles along x axis= x
  let no of tiles along y axis= y
  
  then no of tiles on border=2x+2y-4
  no of tiles in middle= (x-2)(y-2)
  we know that
  (x-2)(y-2)=2x+2y-4
  put the value of x from options one by one and find the value of y
  
  if y is positive integer then that value of x is ans
  
  we will get y=5 for x=2 so (B) is correct option
• 11 years agoHelpfull: Yes(4) No(0)
• let the length of rectangle floor be L and breadth be B and X be the size of one tile
  and N & M be the no. of the tiles along length L and breadth B than NX = L & MX = B
  area of white tiles = area of red tiles = 1/2
  now 2NX^2 + 2(M-2)X^2 =1/2(LB) = 1/2(NX) = 1/2(MNX^2)
  solving this v get that 4M + 4 N - MN = 8
  now looking from the options
  only M = 12 gives integer value of N (that is equal to 5)
• 10 years agoHelpfull: Yes(0) No(0)
• size of room is 12x5 units and tiles are 1x1 unit.
  Total 60 tiles are used.
  out of which 30 tiles are red which are used in (12-2)*(5-2) = 10*3 unit area
  
• 10 years agoHelpfull: Yes(0) No(1)