An engineering apprentice is given a rectangular sheet of metal of dimensions 500mm x 300mm. She is asked to cut out four identical squares, one in each corner of the sheet, fold up the sides and weld the corner seams to make a metal box. What should she make the length of the sides of the squares in order to maximise the volume?

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An engineering apprentice is given a rectangular sheet of metal of dimensions 500mm x 300mm. She is asked to cut out four identical squares, one in each corner of the sheet, fold up the sides and weld the corner seams to make a metal box.
What should she make the length of the sides of the squares in order to maximise the volume?                                           

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