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# A square floor with a side of 3 meters is to be covered with square

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Math Expert
Joined: 02 Sep 2009
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A square floor with a side of 3 meters is to be covered with square [#permalink]

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31 Jan 2018, 00:30
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A square floor with a side of 3 meters is to be covered with square tiles. If each tile has a perimeter of 1 meter, what is the minimum number of tiles needed to cover the floor?

A. 3
B. 9
C. 12
D. 36
E. 144

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A square floor with a side of 3 meters is to be covered with square [#permalink]

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31 Jan 2018, 01:19
Bunuel wrote:
A square floor with a side of 3 meters is to be covered with square tiles. If each tile has a perimeter of 1 meter, what is the minimum number of tiles needed to cover the floor?

A. 3
B. 9
C. 12
D. 36
E. 144

A square floor with side of 3 meters will have an area of $$3^2(9)$$ square meters.

Since the perimeter of the square tile is 1 meter,
the square tile will have a side $$\frac{1}{4}$$ or $$0.25$$ meter and cover an area of $$0.25^2$$ square meter.

Therefore, the total number of tiles needed to cover the entire floor is $$\frac{9}{0.25^2} = 144$$ tiles(Option E)
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Joined: 26 Sep 2017
Posts: 28
Re: A square floor with a side of 3 meters is to be covered with square [#permalink]

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31 Jan 2018, 01:23
Area of floor = 3^2 = 9 sq metres

Side of tile = 1/4 =0.25m

Area of tile = 0.25^2= 0.0625 sq metres

To cover the floor = 9/0.0625= 144

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Posts: 1206
Re: A square floor with a side of 3 meters is to be covered with square [#permalink]

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31 Jan 2018, 03:28
Bunuel wrote:
A square floor with a side of 3 meters is to be covered with square tiles. If each tile has a perimeter of 1 meter, what is the minimum number of tiles needed to cover the floor?

A. 3
B. 9
C. 12
D. 36
E. 144

Solution

• Total area of the square floor $$= 3 * 3 = 9$$ $$meter^2$$

• The perimeter of the square tiles $$= 1$$ meter

o Thus, length of one side of the tile $$= \frac{1}{4}$$ meters

o And area of the square tiles$$= (\frac{1}{4})^2$$ $$meter^2$$

• Let’s assume that n such square tiles are needed to cover the floor

o n * Area of square tiles = Area of the Square Floor

o $$n * \frac{1}{16} = 9$$

o $$n = 16* 9 = 144$$

Thus, the correct answer is Option E.

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Saquib
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Intern
Joined: 08 Aug 2017
Posts: 2
Re: A square floor with a side of 3 meters is to be covered with square [#permalink]

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31 Jan 2018, 03:33
Area of square floor is 9 sq.m.
From perimeter we can find side of the square i.e 1/4 = 0.25m
(no.of tiles)*area of one tile should be = area of square floor.
hence N*0.25*0.25 = 9
so N=144
Option (E)

Regards,
Lalit B.
Re: A square floor with a side of 3 meters is to be covered with square   [#permalink] 31 Jan 2018, 03:33
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