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

Question

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

Show Spoiler

width 4 length 6

pushpitkc · Accepted Answer

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

grichagupta · Answer

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

pushpitkc · Answer

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!

aravindgopalsv · Answer

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purvibagmar · Answer

Not only do we recount all the corner ones, but also all the tiles along the boundary right? I am getting a little confused here

sayan640 · Answer

KarishmaB  ,  chetan2u   GMATCoachBen  Would you like to explain this question ?

chetan2u · Answer

Let the tiles in corner be represented by X and in center by Y, so length would be X YYYY..YY X or L-2 witout corner tiles. Similarly width would be W-2 without corner tiles.
So, sum of tiles on both the length and width without corner tiles would be 2(L-2) + 2(W-2). To get perimeter add the 4 corner tiles.
Perimeter = 2(L-2+W-2)+4 = 16...............2(L+W-4)=12.......L+W-4=6.......L+W=10

Only possible option is 4+6, and as width < length, length = 6 and width = 4.

sayan640 · Answer

Sir , why are you doing ( l -2) ?..Why are you subtracting lengths on either side ? What is the logic behind this...I am struggling to visualize this.

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chetan2u · Answer

Sayan, I am removing the corner tiles, the tiles that touch both length and width. There is a repetition of these tiles as they get calculated once in width and once in length.

So, you could simply have answer as 2(L+B)-4 as perimeter. -4 is the extra tiles of corner that have been calculated in both length and width.

2(L+B)-4=16 or 2(L+B)=20 or L+B=10

GMATinsight · Answer

sayan640 To understand the question, let's assume a chessboard is the kitchen floor . In which case Length, l = 8 Width, b = 8 The number of tiles forming the boundary in that case = 8+8+6+6 = 28 (check figure) Screenshot 2024-06-16 at 11.58.15 AM.png now this is because if you consider 8 tiles in the top and bottom rows then in the two columns you would have only 6 new tiles each forming the perimeter i.e. in each case of the rectangle the total tiles forming the perimeter = l + l + (b-2) + (b-2) = 2(l+b)-4 i.e. 2(l+b)-4 = 16 i.e l + b = 10 Also, l > b so possible answers for l and b from the given table will be 6 and 4 --- GMATinsight | www.GMATinsight.com GMAT FOCUS PREP Expert Youtube: www.Youtube.com/GMATinsight

sayan640 · Answer

Thank you so much ,  GMATinsight  Sir for taking time out to explain in such great detail and clearing all my doubts. Amazing will be an understatement for you

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DishaAgarwal12 · Answer

This is a very good quality question. One tends to think of the formula 2(l+b)=16, and then find the ideal match of l+b, I chose 6,2. But it could also be 5,3. Hence the unique choice. we can choose 6 and 4 because it satisfies the condition l>b. if we chose 5,3; the length would be 5, breadth would be 5 which would make l=b which we don't want

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

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