1. The problem statement, all variables and given/known data The problem is about finding the longest ladder length L that can be carried horizontally across a corner between 2 corridors. 3. The attempt at a solution I understand that the solution's using the Lagrange method but what I don't get is why they can assume that at (a+δ, 0) and (0, b+η) are the points of the longest ladder that touch the sides. I attached a picture to demonstrate an extreme case of what I'm talking about.. (It satisfies the relation ab = ηδ by comparing tan θ.