Renu wants to lay tiles on the floor of her house which is 9m long and 7m wide. Among the following sizes of tiles, which one should she buy so that the floor is tiled without cutting any tile?

Correct option is A

The size of the floor is 9 m × 7 m, which is 900 cm × 700 cm (since 1 m = 100 cm).
To avoid cutting tiles, the dimensions of the tile should perfectly divide the dimensions of the floor. This means the length and width of the floor should be divisible by the length and width of the tile.
Let us check each option:
Option (a): Tile size = 36 cm × 35 cm
· Length: 900÷36=25
· Width: 700÷35=20 Both the dimensions divide perfectly.
Option (b): Tile size = 40 cm × 65 cm
· Length: 900÷40=22.5 (not a whole number)
· Width: 700÷65=10.77 (not a whole number) Hence, these tiles cannot be used without cutting.
Option (c): Tile size = 55 cm × 40 cm
· Length: 900÷55=16.36 (not a whole number)
· Width: 700÷40==17.5 (not a whole number) Hence, these tiles cannot be used without cutting.
Option (d): Tile size = 35 cm × 45 cm
· Length: 900÷35=25.71 (not a whole number)
· Width: 700÷45=15.55 (not a whole number) Hence, these tiles cannot be used without cutting.
Hence, the correct answer is (a) 36 cm × 35 cm.