Number of tiles

Geometry Level 3

A room measuring 3 m × 3 m 3\text{ m}\times 3\text{ m} is tiled with 20 cm × 20 cm 20\text{ cm}\times 20\text{ cm} tiles. How many tiles are there in its two diagonals?

Note: The sides of the tiles are parallel with the sides of the room.


The answer is 29.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

In a square, the number of tiles in one side is equal to the number of tiles in one diagonal. The number of tiles in one side is 300 20 = 15 \frac{300}{20}=15 . So in one diagonal there are also 15 15 tiles.If the number of tiles on side of a square is an odd number, the number of tiles in its 2 2 diagonals is 2 x − 1 2x - 1 where x x is the number of tiles in one side of the square.So the number of tiles in its two diagonal is ( 2 ) ( 15 ) − 1 = 30 − 1 = (2)(15) - 1 = 30 - 1 = 29 \boxed{29}

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