Question

Of all rectangles with perimeter 10 m, which one has the maximum area?

Answer 1

the one that is a square

Answer 2

but how do you get to that?

Answer 3

do you know some calculus?

Answer 4

by symmetry

Answer 5

of course @cwrw238

Answer 6

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

Answer 7

okay

Answer 8

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 \(-\frac{b}{2a}=2.5\)

Answer 9

but really it is more obvious than that
you have a rectangle
largest area is a square by symmetry

Answer 10

oh I see. Thanks for that. I guess that's what i really needed was to just to see it for myself.

Answer 11

yw