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# A rectangular wall area is tiled with 9-inch-by-9-inch decorative squa

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
A rectangular wall area is tiled with 9-inch-by-9-inch decorative squa  [#permalink]

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10 Apr 2018, 05:39
00:00

Difficulty:

45% (medium)

Question Stats:

74% (01:47) correct 26% (01:36) wrong based on 42 sessions

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A rectangular wall area is tiled with 9-inch-by-9-inch decorative square tiles. What is the perimeter of the wall area?

(1) It takes 48 of the square tiles to cover the wall area.
(2) The number of tiles along each of the horizontal boundaries of the wall area is three times the number of tiles along each of the vertical boundaries of the wall area.

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Re: A rectangular wall area is tiled with 9-inch-by-9-inch decorative squa  [#permalink]

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10 Apr 2018, 10:02
Bunuel wrote:
A rectangular wall area is tiled with 9-inch-by-9-inch decorative square tiles. What is the perimeter of the wall area?

(1) It takes 48 of the square tiles to cover the wall area.
(2) The number of tiles along each of the horizontal boundaries of the wall area is three times the number of tiles along each of the vertical boundaries of the wall area.

Let there be 'x' tiles horizontally in each row and 'y' tiles vertically in each column. Then the total number of tiles = x*y.
And perimeter of rectangular wall = 2*(length + width). Since each tile is of 9 inch by 9 inch dimension, perimeter of wall = 2*(9x + 9y) or 18*(x+y).
We need the value of (x+y) to answer this question.

Statement 1:
Total tiles = x*y = 48. But this is not sufficient to find x+y. Because we could have x=8, y=6 or we could have x=12, y=4. These will give different answers to x+y, and thus different perimeters.

Statement 2:
x = 3*y, so perimeter of wall = 18*(3y+y) = 18*4y. But still we need 'y' which we dont have here. Not sufficient.

Combining the statements:
x*y = 48 and x = 3y. So 3y*y = 48 or 3*y^2 = 48 or y^2 = 16 or y=4. Perimeter of wall = 18*4*4. Sufficient.

Re: A rectangular wall area is tiled with 9-inch-by-9-inch decorative squa   [#permalink] 10 Apr 2018, 10:02
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