A rope is swinging in such a way that the length of the arc is decreasing geometrically. If the first arc is 18 feet long and the third arc is 8 feet long, what is the length of the second arc?

Question

anonymous · Answer

are u dizzyy

anonymous · Answer

no

anonymous · Answer

let second rope be x..then x/18 = 8/x
or x^2 = 18 x 8 = 144
x =12...this is the answer

phi · Answer

geometric means you multiply by some factor to get the next number

you start at 18
the next number is 18*K  (K is the factor)
the 3rd number is 18*k*k  
but we know the third number is 8

anonymous · Answer

okay so would 12 be my answer ?

anonymous · Answer

yes ...for sure...12 is the answer

phi · Answer

you can figure it out
18*k*k = 8
divide by 18 on both sides
k*k= 8/18  or 4/9
k= sqrt(4/9) = 2/3

the middle number is k*18

anonymous · Answer

I got it @phi Thank you & Thank you @ritez