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7 January, 04:40

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.

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  1. 7 January, 04:48
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    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.
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