A rectangular field has a length of \( x+3 \) metres and a width of \( x-5 \) metres Determine the value of \( x \) if the perimeter is 24 metres.

To determine the value of \( x \), we can use the formula for the perimeter of a rectangle, which is given by: \[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) \] Plugging in the values for length and width, we have: \[ 2 \times ((x + 3) + (x - 5)) = 24 \] Simplifying this equation: \[ 2 \times (2x - 2) = 24 \] \[ 2x - 2 = 12 \] \[ 2x = 14 \] \[ x = 7 \] So, the value of \( x \) is \( 7 \) metres. --- The concept of perimeter dates back to ancient civilizations, where measuring land for agriculture was essential. The word itself comes from the Greek "peri-" meaning "around" and "metron" meaning "measure"; it has been a fundamental element in geometry for thousands of years! When working on problems involving variables like \( x \), one common mistake is neglecting to distribute correctly or miscalculating terms when combining like terms. Always double-check your arithmetic and step through each part of the equation carefully to avoid errors, especially in the early stages!