Question

Find the perimeter of a square with a side length of 3√32. Your answer must be in simplest radical form.

12 square root of 128

12 square root of 32

16 square root of 3

√482

Answer 1

To find the perimeter of a square, we can use the formula:

\[
P = 4s
\]

where \( s \) is the side length of the square.

Given the side length \( s = 3\sqrt{32} \), we can calculate the perimeter:

\[
P = 4 \times (3\sqrt{32})
\]

Calculating that gives:

\[
P = 12\sqrt{32}
\]

Now, we can simplify \( \sqrt{32} \):

\[
\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}
\]

Substituting this back into the expression for the perimeter:

\[
P = 12\sqrt{32} = 12 \times 4\sqrt{2} = 48\sqrt{2}
\]

So the final answer for the perimeter of the square is:

\[
48\sqrt{2}
\]

Looking at your provided options, it seems like the answers do not match directly. However, if you just needed to confirm the perimeter based on the initial calculations, it would be \( 12\sqrt{32} \) prior to simplification.