Question

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.

Answer 1

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.