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A floorplan for a rectangular kitchen calls for the use of square tile

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A floorplan for a rectangular kitchen calls for the use of square tile  [#permalink]

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New post 03 May 2017, 18:59
A floorplan for a rectangular kitchen calls for the use of square tiles that are exactly one square foot in area, and for aesthetic reasons there can be no partial tiles. If the perimeter of the kitchen is formed by exactly 16 tiles, and the length of the floor is greater than the width, which of the following could be the length and width of the floor, in feet?

Width - Length
2
3
4
5
6
width 4 length 6
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Re: A floorplan for a rectangular kitchen calls for the use of square tile  [#permalink]

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New post 03 May 2017, 19:12
w*l - (w-2)*(l-2) = 16.
Substitute your values in above equation and check which values satisfy
:) .
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Re: A floorplan for a rectangular kitchen calls for the use of square tile  [#permalink]

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New post 12 May 2017, 19:13
can you explain how you come with this formuls
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Re: A floorplan for a rectangular kitchen calls for the use of square tile  [#permalink]

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New post 13 May 2017, 01:33
1
ssr300 wrote:
A floorplan for a rectangular kitchen calls for the use of square tiles that are exactly one square foot in area, and for aesthetic reasons there can be no partial tiles. If the perimeter of the kitchen is formed by exactly 16 tiles, and the length of the floor is greater than the width, which of the following could be the length and width of the floor, in feet?

Width - Length
2
3
4
5
6
width 4 length 6


We know that, the perimeter of the kitchen floor is 16
2 * ( l+b) - 4 = 16 or l+b = 10
This is because the tile at the end will be common for both the length and breadth.
Also, it is known that the length is greater than the breadth(l > b)

The only option from the list which will match both the conditions are
Length : 6 Breadth : 4
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Re: A floorplan for a rectangular kitchen calls for the use of square tile  [#permalink]

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New post 25 May 2017, 09:22
pushpitkc,

Request you to explain why you subtracted 4 from the above equation. I would have formed equation 2(l+w) = 16 and arrived at l=6 and w= 2 which also satisfies the condition that l>w
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Re: A floorplan for a rectangular kitchen calls for the use of square tile  [#permalink]

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New post 25 May 2017, 22:50
1
grichagupta wrote:
pushpitkc,

Request you to explain why you subtracted 4 from the above equation. I would have formed equation 2(l+w) = 16 and arrived at l=6 and w= 2 which also satisfies the condition that l>w


When we try forming a rectangle with exactly 16 tiles, we end up using the tiles at the corner, twice.
Hence, we need to reduce 4(corner tiles) from the total perimeter.

P.S When you try forming a rectangle with 6 tiles as length and 2 tiles as breadth,
you use only 12 tiles(not 16 as asked in the question stem)

Hope its clear!
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Re: A floorplan for a rectangular kitchen calls for the use of square tile &nbs [#permalink] 25 May 2017, 22:50
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