Final answer:
To find the length of each side of the regular hexagon, solve 6(3x + 4) = 96 to find x and substitute it into the expression 3x + 4. The actual length of each side is 16 cm.
Step-by-step explanation:
The student is asking how to determine the length of each side of a regular hexagon where one side is represented as the expression 3x + 4 and the perimeter of the hexagon is 96 cm. Since a regular hexagon has six equal sides, we first divide the perimeter by 6 to find the expression for the length of one side.
Therefore, the equation to solve is 6(3x + 4) = 96.
We simplify the equation:
- Multiply the expression (3x + 4) by 6.
- Equate it to the perimeter of 96 cm.
- Solve for x to find the variable value.
- Substitute the value of x into the expression 3x + 4 to find the actual length of each side.
By following these steps, the value of x is found to be 4.
Substituting this value back into the expression gives us 3(4) + 4, which equals 16 cm.
Therefore, each side of the hexagon is 16 cm long.