Let's go through this problem step by step.
1. Initial Setup:
- The initial height at which the string of flowers is tied on the wall is 20 feet.
- The distance from the wall to the point where the string is tied on the floor is 8 feet.
2. Calculating the Original Length of the String:
- We use the Pythagorean theorem: [tex]\( a^2 + b^2 = c^2 \)[/tex].
- Here, [tex]\( a \)[/tex] is the height (20 feet), [tex]\( b \)[/tex] is the distance from the wall (8 feet), and [tex]\( c \)[/tex] is the length of the string.
- So, [tex]\( c = \sqrt{20^2 + 8^2} \)[/tex].
- This gives [tex]\( c \approx 21.54 \)[/tex] feet.
3. New Setup:
- The height at which the string of flowers is now tied on the wall is 10 feet.
- The length of the string remains the same, so it is still approximately 21.54 feet.
4. Calculating the New Distance From the Wall:
- Using the Pythagorean theorem again, but solving for the distance from the wall:
- Let [tex]\( d \)[/tex] be the new distance from the wall. Then, [tex]\( d \)[/tex] should satisfy the equation [tex]\( 10^2 + d^2 = (21.54)^2 \)[/tex].
- Rearranging for [tex]\( d \)[/tex], we get [tex]\( d = \sqrt{(21.54)^2 - 10^2} \)[/tex].
- This gives [tex]\( d \approx 19.08 \)[/tex] feet.
Therefore, the new distance from the wall where the string would be tied is approximately [tex]\( 19.1 \)[/tex] feet.
So, the correct answer is:
B. [tex]\( 19.1 \)[/tex] feet
