How do you find the maximum area of a rectangle whose perimeter is 100cm?

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Answer 1 · 2015-09-16T00:40:44

Refer to explanation

Let L= length of rectangle
and W=width of rectangle

Hence perimeter is #P=2*(L+W)=>L+W=50=>W=50-L#

The area of rectangle is #A=L*W=>A=L*(50-L)#

The first derivative gives

#(dA)/(dL)=50-2*L=>(dA)/(dL)=0=>L=25#

Hence for #W=L=25# we have the maximum area which is

#A=L*W=25*25=625#