62. The perimeter of a rectangular wooden deck is 90 feet. The deck's length, \( l \), is 5 feet less than 4 times its width, w. Which system of linear equations can be used to determine the dimensions, in feet, of the wooden deck? \( \begin{array}{ll}\text { F } \\ l+w=90 & \text { H } \begin{array}{l}2 l+2 w=90 \\ l=5-4 w\end{array} \\ l=5-4 w \\ \text { G } \\ 2 l+2 w=90 & 3 \\ l=4 w-5 & l+w=90 \\ l=4 w-5\end{array} \)

To determine the dimensions of the rectangular wooden deck, we need to set up a system of linear equations based on the information provided. 1. **Perimeter Equation**: The perimeter \( P \) of a rectangle is given by the formula: \[ P = 2l + 2w \] Given that the perimeter is 90 feet, we can write: \[ 2l + 2w = 90 \] This can be simplified to: \[ l + w = 45 \quad \text{(Equation 1)} \] 2. **Length-Width Relationship**: The problem states that the length \( l \) is 5 feet less than 4 times the width \( w \). This can be expressed as: \[ l = 4w - 5 \quad \text{(Equation 2)} \] Now we have the following system of equations: \[ \begin{align*} 1. & \quad l + w = 45 \\ 2. & \quad l = 4w - 5 \end{align*} \] Looking at the options provided, the correct system of equations that can be used to determine the dimensions of the wooden deck is: \[ \begin{align*} l + w = 45 \\ l = 4w - 5 \end{align*} \] Thus, the answer is: \[ \text{G: } 2l + 2w = 90 \quad \text{and} \quad l = 4w - 5 \]