Question

what is the length of the diagonal of a square with a perimeter 32

Answer 1

To find the length of the diagonal of a square with a perimeter of 32, we first need to determine the length of one side of the square.

The formula for the perimeter \( P \) of a square is given by:

\[
P = 4s
\]

where \( s \) is the length of one side. Given that the perimeter is 32, we can set up the equation:

\[
4s = 32
\]

Now, solving for \( s \):

\[
s = \frac{32}{4} = 8
\]

Now that we have the side length of the square, we can find the length of the diagonal \( d \) using the formula for the diagonal of a square:

\[
d = s\sqrt{2}
\]

Substituting \( s = 8 \):

\[
d = 8\sqrt{2}
\]

Therefore, the length of the diagonal of the square is \( 8\sqrt{2} \). If you need a numerical approximation:

\[
8\sqrt{2} \approx 8 \times 1.414 \approx 11.314
\]

So, the exact length of the diagonal is \( 8\sqrt{2} \), or approximately \( 11.314 \).