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

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

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New post 30 Jan 2018, 23:30
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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
[Reveal] Spoiler: OA

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

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New post 31 Jan 2018, 00:19
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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Re: A square floor with a side of 3 meters is to be covered with square [#permalink]

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New post 31 Jan 2018, 00:23
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

Answer E

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

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New post 31 Jan 2018, 02:28
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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Re: A square floor with a side of 3 meters is to be covered with square [#permalink]

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New post 31 Jan 2018, 02:33
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)


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Lalit B.
Re: A square floor with a side of 3 meters is to be covered with square   [#permalink] 31 Jan 2018, 02:33
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