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Of all rectangles with perimeter 10 m, which one has the maximum area?
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the one that is a square
but how do you get to that?
do you know some calculus?
by symmetry
of course @cwrw238
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you can call one side \(x\) and the other side \(y\) but you cannot tell \(x\) from \(y\) and so there is no difference between them
okay
or you can call one side \(x\) and the other side \(y\) then you kbnow \[2x+2y=10\] or \[y=5-x\] and maximize \[x(5-x)=5x-x^2\] max is at the vertex, namely \(-\frac{b}{2a}=2.5\)
but really it is more obvious than that you have a rectangle largest area is a square by symmetry
oh I see. Thanks for that. I guess that's what i really needed was to just to see it for myself.
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yw
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