A rectangular floor measures 3m by 2m is covered by 384 square tiles. Determine the side length of each tile in centimeters.
The rectangular floor measures 3m by 2m. The area of the floor is 6 m^2. It is covered by 384 square tiles. If the side length of each tile is x cm., the area of one tile is x^2*10^-4 m^2
This gives 384*x^2*10^-4 = 6
=> x^2 = 6*10^4/384
=> x^2 = 60000/384
=> x^2 = 156.25
=> x = 12.5
The length of the side of the tiles is 12.5 cm.
Floor area = 3m * 2m = 6 m2
No. of tiles covering the floor = 384
Area of each tile = 6/384 = 0.012525 m2 = 125.25 cm2
let x be the side length of a tile in cm
x^2 = 125.25 cm2
x = 12.5 cm
Length of the side of a tile is 12.5 cm
Let the no. of tiles in lengthwise be 'x'.
length of the room is 3 metres=300 cm
Hence length of the side of each tile = 300/x cm.
Let the no. of tiles in breadthwise be 'y'.
breadth of the room is 2 metres = 200 cm.
Hence length of the side of each tile = 200/y cm.
Since the tiles are square 300/x = 200/y
Hence x/3 = y/2 or x= 3/2y.
Total no. of tiles=xy=384.
3/2 y^2 =384
y^2 =384 * 2/3 =256
no. of tiles =24*16 =384 (verified)
Hence length of the side of each tile = 300/24 =100/8=12.5 cm.
Answer: side length of each tile = 12.5 cm.