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A six-sided mosaic contains 24 triangular pieces of tile of the same

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A six-sided mosaic contains 24 triangular pieces of tile of the same  [#permalink]

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New post 26 Apr 2019, 03:01
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A
B
C
D
E

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74% (01:25) correct 26% (01:37) wrong based on 82 sessions

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A six-sided mosaic contains 24 triangular pieces of tile of the same size and shape, as shown in the figure above. If the sections of tile fit together perfectly, how many square centimeters of tile are in the mosaic?

(1) Each side of each triangular piece of tile is 9 centimeters long.
(2) The mosaic can be put inside a rectangular frame that is 40 centimeters wide.


DS24602.01
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2019-04-26_1400.png
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Re: A six-sided mosaic contains 24 triangular pieces of tile of the same  [#permalink]

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New post 26 Apr 2019, 15:10
The Logical approach to this question will focus on looking for the length of the side of one tile, since one side is enough in order to find the area of an equilateral triangle.
Statement (1) gives us just what we were looking for. Answer choices (B), (C) and (E) are eliminated.
Statement (2) doesn’t an exact measure, and as we're not told whether it is inscribed or not. Answer choice (D) is also eliminated.
The correct answer is (A).

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Re: A six-sided mosaic contains 24 triangular pieces of tile of the same  [#permalink]

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New post 27 Apr 2019, 08:03
Bunuel wrote:
Image
A six-sided mosaic contains 24 triangular pieces of tile of the same size and shape, as shown in the figure above. If the sections of tile fit together perfectly, how many square centimeters of tile are in the mosaic?

(1) Each side of each triangular piece of tile is 9 centimeters long.
(2) The mosaic can be put inside a rectangular frame that is 40 centimeters wide.


DS24602.01
OG2020 NEW QUESTION


Attachment:
2019-04-26_1400.png


#1
hexagon is 6 times equilateral ∆ area
given side = 9 sufficeint to solve
#2
mosaic rectangluar size ; insufficeint
IMO A
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Re: A six-sided mosaic contains 24 triangular pieces of tile of the same  [#permalink]

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New post 27 Apr 2019, 19:18
Bunuel wrote:
Image
A six-sided mosaic contains 24 triangular pieces of tile of the same size and shape, as shown in the figure above. If the sections of tile fit together perfectly, how many square centimeters of tile are in the mosaic?

(1) Each side of each triangular piece of tile is 9 centimeters long.
(2) The mosaic can be put inside a rectangular frame that is 40 centimeters wide.


DS24602.01
OG2020 NEW QUESTION


Let \(A\) be the area of the mosaic. The original question: \(A=?\)

1) We know that the small tiles are equilateral triangles with side lengths of 9. Since the formula for the height of an equilateral triangle is \(height=\frac{\sqrt{3}}{2}\cdot base\), the area of the mosaic is the following.

\(A=24\cdot \frac{9\cdot \frac{\sqrt{3}}{2}\cdot 9}{2}\)

Thus, the answer to the original question is a unique value. \(\implies\) Sufficient

2) We know that the frame in which the mosaic is placed is 40 cm wide, but no information is given about the side lengths of the 24 identical triangles. Even if the bases of these identical isosceles triangles were given, different heights would give us different areas. Thus, we can't get a unique value to answer the original question. \(\implies\) Insufficient

Answer: A
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Re: A six-sided mosaic contains 24 triangular pieces of tile of the same  [#permalink]

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New post 12 May 2019, 14:11
Hi All,

We're told that a six-sided mosaic contains 24 triangular pieces of tile of the SAME size and shape, as shown in the figure above and that the sections of tile fit together perfectly. We're asked for the total square centimeters of tile in the mosaic. While this question might look a bit 'crazy', it's a great "concept question" meaning that if you know the concepts involved, then you won't have to do much math to actually get the correct answer. To answer this question, we'll need information to determine the area of any one of the triangles, then we can multiply that area by 24 to get the total area of the mosaic.

1) Each side of each triangular piece of tile is 9 centimeters long.

Fact 1 tells us that we're dealing with Equilateral triangles with sides of 9 cm. With this information, we can determine the area of each triangular tile (the best part is that we don't actually have to do that math here; we know that we CAN do that math - and that there will be just one value for the area - so we can stop working).
Fact 1 is SUFFICIENT

2) The mosaic can be put inside a rectangular frame that is 40 centimeters wide.

The information in Fact 2 puts a limit on what the maximum side of each triangle could be, but doesn't given us any data on the exact areas involved, so since the triangles don't have a set area, the answer to the question will change as the areas change.
Fact 2 is INSUFFICIENT

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Re: A six-sided mosaic contains 24 triangular pieces of tile of the same   [#permalink] 12 May 2019, 14:11
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