I am having a little bit of trouble with one of my math problems.(adsbygoogle = window.adsbygoogle || []).push({});

a) A rectanglewith length L and width W is cut in to four smaller rectangles by two lines parallel to the sides. Find the minimum value of the sum of the squares of the areas of the smaller rectangles.

b) Show that the maximum of the sum of the squares of the areas occurs when cutting lines correspond to sides of the rectangle (so that there is only one rectangle).

i started part a) and this is what i got so far:

A=LW , A(small)=a , a=1/4*LW

so da/dL = (1/4)*W and da/dW= (1/4)*L

and the sum of the squares of all these are equal to 0 so

4[1/16(L^2+W^2)] = 0

1/4(L^2+W^2) = 0

I dont think that this is right though, can anyone help me out here?

thanks

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# Homework Help: Minimizing with partials

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