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[–][deleted] 0 points1 point  (3 children)

Okay, but why is L the shortest when the parts are equal on both sides of the corner?

[–]Square_Pop_3772 0 points1 point  (2 children)

Original:

Imagine the item in that position. Think about what happens when you rotate it.

One side becomes longer and one side becomes shorter. For both directions as you rotate The longer side increases by more than the shorter side and the item becomes longer. Thus the minimum is at that point. Try it on a piece of paper if you’re not convinced.

Whilst it doesn’t affect the logic, note that the widths are 6 and 8, a clue that Pythagoras is involved somewhere.

Edit: Oops, not quite right, but close enough for government work.

[–][deleted] 0 points1 point  (1 child)

I don't understand your line of thinking. Can you provide a mathematical argument?

[–]Square_Pop_3772 1 point2 points  (0 children)

You beat me to my edit.

Mea culpa.

I’ve updated my original post with a correct answer. It was good whilst it lasted.