I really just need help with this problem, I seem to just get confused on how to

Question

I really just need help with this problem, I seem to just get confused on how to set up the two equations to each other!

You are to build a box whose height is 0.440 times its length. In order for the box to have a given volume while using a minimum amount of cardboard, what should be the ratio of the width of the box to its length? (There are six surfaces.)

I Know that you need to set up the volume in terms of L and i know the surface area equation. It is just putting it all together and i'm so confused!

Explanation / Answer

h=0.44 l
let w be the width

then volume = h*l*w = 0.44l*l*w
area minimum
Area= 2(hl+lw+wh) = 2(0.44l2 + lw+ 0.44lw) = 2(0.44l2 +1.44lw)

for minimum d area/dl = 0

2(0.88l+1.44w) =0

w/l=0.88/1.44 = 0.61111

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