peice of metal

Question

an open box is to be constructed from a peice of sheet metal by removing a square of side 2 feet from each cornor and turning up the edges. if the peice of metal is rectangle whose length is twice its width and if the box is to hold 50 cubic feet what should the length and the width of the sheet metal be

Answer 1

Volume = V = (L-4)(W-4)H = (2W-4)(W-4)(2) = (2W^2 -12W +16)(2) =50

W^2 -6W + 8 = 25/2

W^2-6W + 9 = 9-8+25/2 = 1+25/2 = 27/2

(W-3)^2 = 27/2

W-3 = sqr(27/2)

W = 3 + sqr(27/2) = about 6.67 feet wide

L = 2(6.67) = 13.35 feet long

V = 2.57(9.35)(2) = 50