Question

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?

Answer 1

The correct answer to this question is this one:

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

So x = 12.

Answer 2

Answer: The length of the second arc is 12 feet.

Step-by-step explanation:

Since we know that

A rope is swinging in such a way that the length of the arc is decreasing geometrically,

Length of first arc = 18 feet

Length of third arc = 8 feet

Let the length of second arc be x

As we know that

$\frac{a_2}{a_1}=\frac{a_3}{a_2}\\\\\frac{x}{18}=\frac{8}{x}\\\\x^2=18\times 8\\\\x^2=144\\\\x=\sqrt{144}\\\\x=12$

Hence, the length of the second arc is 12 feet.