# A rectangular floor measures 3m by 2m is covered by 384 square tiles. Determine the side length of each tile in centimeters.

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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.

3/2y.y=384

3/2 y^2 =384

y^2 =384 * 2/3 =256

y=16

Hence x=24

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.