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High.
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Let x, y, z be the length, width and height of the box respectively.
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Let volume v is equal to 1728 cm3 which means that x, y, z equal to 1728.
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Therefore, z is equal to 1728 upon x, y.
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Now surface area is given by twice of x, y plus y, z plus z, x.
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Substituting z value in surface area we get this is equal to twice of x, y plus y into 1728 x, y plus 1728 upon x, y into x.
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So that will be equal to, we can say this as a f of x, y and f of x, y will be equal to 2 into x, y plus 1728 upon x plus 1728 upon y.
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That f of x, differentiating with respect to x, we get 2 into 1 into y minus 1728 upon x square plus 0 which is equal to 2 into y minus 1728 upon x square and differentiating with respect to y, we get this is equal to 2 into x into 1 plus 0 minus 1728 upon y square which is equal to 2 into x minus 1728 upon y square.
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Now equating both of them to 0, we get fx is equal to twice of y minus 1728 upon x square equal to 0 which implies that x square equal to 1728 upon y square and therefore upon y, not y square, therefore x is equal to 24 root 3 upon y...