Find the least number A such that for any two squares of combined area 1, a rectangle of area A exists such that the two squares can be packed in the rectangle (without interior
overlap).
You may assume that the sides of the squares are parallel to the sides of the
rectangle.
(In reply to
Second attempt by Larry)
I think you are still misreading the problem. It's asking for the smallest rectangle that will guarantee any two squares with combined area 1 will fit inside.
Clearly one side needs to be at least 1, because one of the two squares can be this large. (I fully agree with Charlie's answer of sqrt(2).)
You are trying to maximize a quantity, which shows you are not answering the question that asks for the least area. You are answering a question something like:
Given two squares whose areas sum to 1, there is a minimum rectangle they will fit inside. For what two squares is this minimum greatest?
My desmos graph for comparison. Note my a is the area, where you used A fr side length.
https://www.desmos.com/calculator/wt4vbp49qi
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Posted by Jer
on 2024-04-02 10:50:16 |
re: Second attempt
