Question

Find the perimeter of a square with a side length of 3sqrt(32) Your answer must be in simplest radical form (1 point ) 12sqrt(128); 16sqrt(3); 12sqrt(32); 48sqrt(2)

Answer 1

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

\[
\text{Perimeter} = 4 \times \text{side length}
\]

Given the side length of the square is \( 3\sqrt{32} \), we can substitute this value into the formula:

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

Calculating this gives:

\[
\text{Perimeter} = 12\sqrt{32}
\]

Next, we need to simplify \( \sqrt{32} \):

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

Now, we can substitute back into the perimeter calculation:

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

Thus, the perimeter of the square is:

\[
\boxed{48\sqrt{2}}
\]