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Math Help - Maximum size rectangle that can fit inside a square

  1. #1
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    Maximum size rectangle that can fit inside a square

    Hello all

    Thanks for all the help ahead of time.


    To put some story into place-i am refinishing/rebuilding a 125g saltwater fishtank system. It was a very nice custom built cabinet but came with some very small doors. I want to install a smaller tank in the cabinet below for various purposes but want to maximize the size of the tank.

    The cabinet has 2 doors (see here for pictures if you need http://i85.photobucket.com/albums/k6...Tank/tank2.jpg ). As i said, i want to maximize the size of the tank i am putting underneath. I am looking to build a plexiglass tank as large as i can to hold as much water as possible under the main tank.

    The window dimensions are 20" tall 16.5" across the top and i would have about 17" of depth before i hit the wall inside. Please dont worry about anything inside as it is currently empty.

    Thanks ~!
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  2. #2
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    Quote Originally Posted by businessguymax View Post
    Hello all

    Thanks for all the help ahead of time.


    To put some story into place-i am refinishing/rebuilding a 125g saltwater fishtank system. It was a very nice custom built cabinet but came with some very small doors. I want to install a smaller tank in the cabinet below for various purposes but want to maximize the size of the tank.

    The cabinet has 2 doors (see here for pictures if you need http://i85.photobucket.com/albums/k6...Tank/tank2.jpg ). As i said, i want to maximize the size of the tank i am putting underneath. I am looking to build a plexiglass tank as large as i can to hold as much water as possible under the main tank.

    The window dimensions are 20" tall 16.5" across the top and i would have about 17" of depth before i hit the wall inside. Please dont worry about anything inside as it is currently empty.

    Thanks ~!
    1. If I understand your problem correctly you are looking for the dimensions of the tank such that you can thread it through the hole into the cabinet and that it holds as much water as possible.(?)

    2. If so: The tank has to have a maximum height of 20''. Then the volume depends on the dimension of the base area.

    3. The base area is calcuated by:

    a = x \cdot y

    The lengthes x and y are calculated by:

    x = 16.5 \cdot \sin(A)

    y = \frac{17}{\sin(A)}

    Therefore

    a = 16.5 \cdot \sin(A) \cdot \dfrac{17}{\sin(A)}= 16.5 \cdot 17

    4. If I didn't make one of my silly mistakes the volume of the tank is a constant. So you only can choose for a convenient angle A such that the construction isn't too hard.
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