(6) The perimeter of a rectangular garden is 114 feet. The width is five leet less than the length, which syxtem of equations could be used to deternine the dimensions of the garden?

To determine the dimensions of the rectangular garden, we can set up a system of equations based on the information provided. **Let:** - \( L \) = Length of the garden (in feet) - \( W \) = Width of the garden (in feet) **Given:** 1. **Perimeter of the garden is 114 feet.** The formula for the perimeter (\( P \)) of a rectangle is: \[ P = 2L + 2W \] Substituting the given perimeter: \[ 2L + 2W = 114 \quad \text{(Equation 1)} \] 2. **The width is five feet less than the length.** This relationship can be expressed as: \[ W = L - 5 \quad \text{(Equation 2)} \] **System of Equations:** \[ \begin{cases} 2L + 2W = 114 \\ W = L - 5 \end{cases} \] **Solving the System:** 1. **Substitute Equation 2 into Equation 1:** \[ 2L + 2(L - 5) = 114 \] 2. **Simplify and solve for \( L \):** \[ 2L + 2L - 10 = 114 \\ 4L - 10 = 114 \\ 4L = 124 \\ L = 31 \text{ feet} \] 3. **Find \( W \) using Equation 2:** \[ W = 31 - 5 = 26 \text{ feet} \] **Dimensions of the Garden:** - **Length:** 31 feet - **Width:** 26 feet **Answer:** \[ \begin{cases} 2L + 2W = 114 \\ W = L - 5 \end{cases} \]