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I want to calculate the maximum measurements that a wooden board can have, to pass through the corner

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The first thing I did was to make a problem easier, when the table does not have width, with similar triangles, calculating the red line (the maximum length that the table can have). I got a function and I minimized it. enter image description here enter image description here

But I do not know how to do when the wood has an area. I imagine it is a minimization problem with two variables, but I do not know what function to use, help me please

Beth
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  • I think you mean the maximum measurements that a board can have, not must have, to pass through the hallway. Then you need to define maximum. Do you mean maximum area? You found the maximum length. Do you mean maximum length given the width? Or what? – Ross Millikan Feb 12 '19 at 05:09
  • Yes, sorry I dont speak english very well, but I try to find the maximum measurements that a board can have, and I have found the maximum length – Beth Feb 12 '19 at 05:12
  • Other approaches to the simple version of the problem are here: https://math.stackexchange.com/questions/583707/intuitive-explanation-for-formula-of-maximum-length-of-a-pipe-moving-around-a-co -- perhaps one can be adapted for the case where the board has width as well as length. – David K Feb 12 '19 at 05:23
  • See https://math.stackexchange.com/questions/2922887 – cgiovanardi Feb 12 '19 at 23:11

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Let the board have width $W$. Use the same technique to compute the maximum length $L$ as a function of $W$. It won't be nearly as clean because the effective length of the board depends on the width. Now use $A=LW$ and substitute in the expression for one variable in terms of the other. Now you have $A$ as a function of one variable, so take the derivative, set to zero...

Ross Millikan
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