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A rectangular room having dimensions 3.74 m x 5.78 m is required to be tiled using minimum number of identical square tiles. The number of such tiles and area of each tile (in cm2) is given by;
  • a)
    176 and 867
  • b)
    143 and 961
  • c)
    187 and 1156
  • d)
    198 and 1024
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A rectangular room having dimensions 3.74 m x 5.78 m is required to be...
In this question, we need to find the HCF of 374 and 578 which is 34. We can look at 374 = 34 x 11 and 578 = 34 x 17. This gives the number of square tiles required to cover the entire room is 11 x 17 = 187 and area of each such tile is 342 = 1156 cm2.
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A rectangular room having dimensions 3.74 m x 5.78 m is required to be...
To find the minimum number of identical square tiles required to tile a rectangular room, we need to divide the area of the room by the area of each tile.

Given dimensions of the room: 3.74 m x 5.78 m

Step 1: Convert the dimensions to centimeters
Multiply the length and width by 100 to convert from meters to centimeters.
Length = 3.74 m * 100 cm/m = 374 cm
Width = 5.78 m * 100 cm/m = 578 cm

Step 2: Calculate the area of the room
Area = Length * Width = 374 cm * 578 cm = 216172 cm^2

Step 3: Calculate the area of each tile
Given area of each tile = 1156 cm^2

Step 4: Calculate the minimum number of tiles required
Number of tiles = Area of room / Area of each tile
Number of tiles = 216172 cm^2 / 1156 cm^2 = 187

Therefore, the correct answer is option C: 187 tiles with an area of each tile being 1156 cm^2.
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A rectangular room having dimensions 3.74 m x 5.78 m is required to be tiled using minimum number of identical square tiles. The number of such tiles and area of each tile (in cm2) is given by;a)176 and 867b)143 and 961c)187 and 1156d)198 and 1024Correct answer is option 'C'. Can you explain this answer?
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