Ask Question
4 June, 01:35

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.

+1
Answers (1)
  1. 4 June, 03:24
    0
    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.
Know the Answer?
Not Sure About the Answer?
Find an answer to your 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 ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers