Consecutive members

The block has a volume of 1728 cm³. Determine the lengths of the edges a, b, c of the blocks for which a < b < c and a + b + c = 38 cm and whose numerical values in cm represent three consecutive members of the geometric sequence.

Correct result:

a =  8 cm
b =  12 cm
c =  18 cm

Solution:

V=1728 cm3  1728=26×33  V=abc b=qa c=q2a a+b+c=38  V=a aq aq2=a3 q3=(aq)3 a q=V3=17283=12  a aq (38aaq)=V a12(38a12)=V  a 12 (38a12)=1728 12a2+312a1728=0 12a2312a+1728=0  p=12;q=312;r=1728 D=q24pr=31224121728=14400 D>0  a1,2=q±D2p=312±1440024 a1,2=312±12024 a1,2=13±5 a1=18 a2=8   Factored form of the equation:  12(a18)(a8)=0  a=a2=8=8 cm q=12/a=12/8=32=1.5

Our quadratic equation calculator calculates it.

b=q a=1.5 8=12 cm
c=q b=1.5 12=18 cm



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