He perimeter of a rectangle is 64 cm. find the lengths of the sides of the rectangle giving the maximum area. enter the answers for the lengths of the sides in increasing order.

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.