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The water tank shown above is a prism, consisting of 3 rectangular fac
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05 Feb 2019, 12:03
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Difficulty:
85% (hard)
Question Stats:
39% (02:48) correct 61% (03:27) wrong based on 38 sessions
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The water tank shown is a prism with 3 rectangular faces and 2 equilateral triangular faces. Each triangular face has height 6, and the water surface is parallel to the face ABCD. If the volume occupied by the water is half the volume of the water tank, which of the following is closest to the length of x ?
Re: The water tank shown above is a prism, consisting of 3 rectangular fac
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05 Feb 2019, 15:14
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volume of the prism tank = area of side triangle * length of tank
volume of water = \(\frac{1}{2}\) volume of whole tank
(area of triangle with height x)*(length of tank) = \(\frac{1}{2}\) (area of triangle with height 6)*(length of tank)
(area of triangle with height x) = \(\frac{1}{2}\) (area of triangle with height 6)
because the water surface is parallel to the ABCD face of the tank, the two triangles are similar (AAA)
similar triangles have side ratio = \(\frac{x}{y}\) and area ratio of \(\frac{x^2}{y^2}\)
in our case, the ratio of areas = \(\frac{(area-of-triangle-with-height-x)}{(area-of-triangle-with-height-6)}\) = \(\frac{1}{2}\) = \(\frac{x^2}{y^2}\)
so the ratio of sides = \(\frac{x}{y}\) = \(\frac{1}{\sqrt{2}}\)
knowing that the bigger triangle has height 6, then \(x\) = \(\frac{6}{\sqrt{2}}\) = \(\frac{6\sqrt[]{2}}{2}\) = \(3\sqrt[]{2}\) = \(3*1.4\) \(\approx\) \(4.2\)
The water tank shown above is a prism, consisting of 3 rectangular fac
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06 Feb 2019, 06:07
fskilnik wrote:
The water tank shown is a prism with 3 rectangular faces and 2 equilateral triangular faces. Each triangular face has height 6, and the water surface is parallel to the face ABCD. If the volume occupied by the water is half the volume of the water tank, which of the following is closest to the length of x ?
(A) 1.73 (B) 2.83 (C) 3.46 (D) 4.24 (E) 5.20
GMATH practice exercise (Quant Class 17)
Very good, Mahmoudfawzy83 ! Congrats (kudos!) and thank you for your contribution!
Let me offer our "official solution": (It is only different of yours in the "wording".)
The triangles we are comparing between are similar to each other. the meaning of 'similar triangles' is that they their corresponding angles are equal. in our case both triangles has angles of 60 degree each. If two triangles are proved to be similar, the the ratio between any side and its corresponding side in the other triangle = \(\frac{x}{y}\) and it can be deduced the ratio between the ares of the two triangles = \(\frac{x^2}{y^2}\)
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39% (02:48) correct 
