Question

If Athena designs a circular hedge with a diameter equal to 9 square root of 5
feet, which of these describes the upper and lower boundaries for the estimated length of the hedge's diameter?

A circular hedge with diameter 9 square root 5 feet.
Select an answer

9 ft. to 18 ft.
18 ft. to 27 ft.
27 ft. to 36 ft.
36 ft. to 45 ft.

Answer 1

To find the upper and lower boundaries for the estimated length of the hedge's diameter, we need to evaluate the value of the diameter given, which is \(9 \sqrt{5}\) feet.

First, we calculate \(9 \sqrt{5}\):

Using the approximate value of \(\sqrt{5} \approx 2.236\),

\[
9 \sqrt{5} \approx 9 \times 2.236 \approx 20.124 \, \text{feet}
\]

Next, we consider the estimated boundaries for this length. The calculated value \(20.124\) feet falls between the options provided.

Now let's evaluate the options:

- \(9 \, \text{ft} \text{ to } 18 \, \text{ft}\) - This does not include \(20.124\).
- \(18 \, \text{ft} \text{ to } 27 \, \text{ft}\) - This includes \(20.124\).
- \(27 \, \text{ft} \text{ to } 36 \, \text{ft}\) - This does not include \(20.124\).
- \(36 \, \text{ft} \text{ to } 45 \, \text{ft}\) - This does not include \(20.124\).

Therefore, the correct option that describes the upper and lower boundaries for the estimated length of the hedge's diameter is:

**18 ft. to 27 ft.**