mbrisen1 mbrisen1

20-02-2017
Mathematics

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What is the largest possible area for a rectangle with a perimeter of 40 cm?

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nikita83 nikita83

20-02-2017

[tex]p=2(a+b)=40\\S=ab=a(p/2-a)=ap/2-a^2\\S'=p/2-2a=0\quad\Rightarrow\quad a=p/4=10,b=p/2-a=p/4=10\\S_{\max}=100[/tex]

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