Question

Find the length of one side of a regular hexagon, if its perimeter is 24x + 48.

Answer 1

A regular hexagon has six equal sides. The perimeter \( P \) of a regular hexagon can be calculated using the formula:

\[
P = 6s
\]

where \( s \) is the length of one side. Given the perimeter is \( 24x + 48 \), we can set up the equation:

\[
6s = 24x + 48
\]

To find the length of one side \( s \), we will divide both sides of the equation by 6:

\[
s = \frac{24x + 48}{6}
\]

Now, simplify the right side:

\[
s = \frac{24x}{6} + \frac{48}{6} = 4x + 8
\]

Thus, the length of one side of the hexagon is:

\[
\boxed{4x + 8}
\]