4. Multiple Choice 1 point 4. Greg is making a rectangular garden. He has purchased 84 feet of fencing. What length \( (\mathrm{L}) \) and width \( (\mathrm{W}) \) will maximize the area of a garden with a perimeter of 84 feet? \( \mathrm{L}=64 \mathrm{ft}, \mathrm{W}=20 \mathrm{ft} \). \( \mathrm{L}=32 \mathrm{ft}, \mathrm{W}=10 \mathrm{ft} \). \( \mathrm{L}=42 \mathrm{ft}, \mathrm{W}=42 \mathrm{ft} \). \( \mathrm{L}=21 \mathrm{ft}, \mathrm{W}=21 \mathrm{ft} \).

To determine which dimensions maximize the area of Greg's rectangular garden with a perimeter of 84 feet, let's analyze the options: 1. **\( \mathrm{L}=64 \mathrm{ft}, \mathrm{W}=20 \mathrm{ft} \)** - **Perimeter**: \( 2 \times 64 + 2 \times 20 = 128 + 40 = 168 \) ft *(Exceeds 84 ft)* 2. **\( \mathrm{L}=32 \mathrm{ft}, \mathrm{W}=10 \mathrm{ft} \)** - **Perimeter**: \( 2 \times 32 + 2 \times 10 = 64 + 20 = 84 \) ft - **Area**: \( 32 \times 10 = 320 \) sq ft 3. **\( \mathrm{L}=42 \mathrm{ft}, \mathrm{W}=42 \mathrm{ft} \)** - **Perimeter**: \( 2 \times 42 + 2 \times 42 = 168 \) ft *(Exceeds 84 ft)* 4. **\( \mathrm{L}=21 \mathrm{ft}, \mathrm{W}=21 \mathrm{ft} \)** - **Perimeter**: \( 2 \times 21 + 2 \times 21 = 84 \) ft - **Area**: \( 21 \times 21 = 441 \) sq ft The **maximum area** is achieved when the garden is a square, which in this case is **21 ft by 21 ft**. **Answer:** \( \mathrm{L}=21 \mathrm{ft}, \mathrm{W}=21 \mathrm{ft} \).