Paper box

The hard rectangular paper has dimensions of 60 cm and 28 cm. We cut off the corners into equal squares, and the residue was bent to form an open box. How long must beside the squares be the largest volume of the box?

Correct answer:

c =  6 cm

Step-by-step explanation:

a=60 b=28 V = (a2c)(b2c)c V = (602c)(282c)c V = 4c3176c2+1680c V = 12c2 352c +1680 V = 0 12c2352c+1680=0  12c2352c+1680=0 12=223 352=2511 1680=24357 GCD(12,352,1680)=22=4  3c288c+420=0  p=3;q=88;r=420 D=q24pr=88243420=2704 D>0  c1,2=2pq±D=688±2704 c1,2=688±52 c1,2=14.666667±8.666667 c1=23.333333333 c2=6 c=c1=23.3333=6 a1=a2 c1=602 23.3333=34013.3333 b1=b2 c1=282 23.3333=35618.6667 V1=a1 b1 c1=13.3333 (18.6667) 23.33335807.4074 a2=a2 c2=602 6=48 b2=b2 c2=282 6=16 V2=a2 b2 c2=48 16 6=4608 V2 > V1 c=c2=6=6 cm

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