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