Formula for perimeter of a rectangle is: P = 2 * (a+b) This means that sum of two sides is: 64 = 2* (a+b) a+b=32
Pairs of numbers that add to 32 are: 1+31 2+30 3+29 4+28 5+27 6+26 7+25 8+24 9+23 10+22 11+21 12+20 13+19 14+18 15+17 16+16 We do not consider last pair as it would represent square. Areas these sides cover are: 1*31=31 2*30=60 3*29=87 4*28=112 5**27=135 6*26=156 7*25=175 8*24=192 9*23=207 10*22=220 11*21=231 12*20=240 13*19=247 14*18=252 15*17=255
Maximum area is 255 and lengths of sides are 15 and 17. This answer makes sense because larger sides give larger area.
