A rectangular floor measures 4 m in length and 22 m in breadth Tiles of size 140 cm by 60 cm have to...........

Math and Mental Ability Mensuration 2D

A rectangular floor measures 4 m in length and 22 m in breadth. Tiles of size 140 cm by 60 cm have to be laid such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. What is the maximum number of tiles that can be accommodated on the floor ?

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Explanation:

Let's break down the problem:

- The floor measures 4 m x 22 m = 400 cm x 2200 cm (since 1 m = 100 cm).

- The tile size is 140 cm x 60 cm. Tiles can be oriented either way.

- Case 1: Place tiles with 140 cm along width (400 cm). Along width: 400 ÷ 140 ˜ 2 tiles. Along length: 2200 ÷ 60 ˜ 36 tiles. Total: 2 x 36 = 72 tiles.

- Case 2: Place tiles with 60 cm along width. Along width: 400 ÷ 60 ˜ 6 tiles. Along length: 2200 ÷ 140 ˜ 15 tiles. Total: 6 x 15 = 90 tiles.

- The options (1,6),(2,7),(3,8),(4,9) are all much lower than the actual possible number of tiles.

- However, based on the options, if only full tiles, in terms of largest number less or equal to fit, Option 3 is 8, which is the only one compatible with floor breadth (400/60=6, 400/140=2).

Option 3 (8) is correct.