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? $$ \mathrm{L}=64 \mathrm{ft}, \mathrm{W}=20 \mathrm{ft} $$. $$ \mathrm{L}=32 \mathrm{ft}, \mathrm{W}=10 \mathrm{ft} $$. $$ \mathrm{L}=42 \mathrm{ft}, \mathrm{W}=42 \mathrm{ft} $$. $$ \mathrm{L}=21 \mathrm{ft}, \mathrm{W}=21 \mathrm{ft} $$.

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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**: $$ 2 	imes 64 + 2 	imes 20 = 128 + 40 = 168 $$ ft *(Exceeds 84 ft)*
   
2. **$$ \mathrm{L}=32 \mathrm{ft}, \mathrm{W}=10 \mathrm{ft} $$**
   - **Perimeter**: $$ 2 	imes 32 + 2 	imes 10 = 64 + 20 = 84 $$ ft
   - **Area**: $$ 32 	imes 10 = 320 $$ sq ft
   
3. **$$ \mathrm{L}=42 \mathrm{ft}, \mathrm{W}=42 \mathrm{ft} $$**
   - **Perimeter**: $$ 2 	imes 42 + 2 	imes 42 = 168 $$ ft *(Exceeds 84 ft)*
   
4. **$$ \mathrm{L}=21 \mathrm{ft}, \mathrm{W}=21 \mathrm{ft} $$**
   - **Perimeter**: $$ 2 	imes 21 + 2 	imes 21 = 84 $$ ft
   - **Area**: $$ 21 	imes 21 = 441 $$ sq ft

The **maximum area** is achieved when the garden is a square, which in this case is **21 ft by 21 ft**.

**Answer:** $$ \mathrm{L}=21 \mathrm{ft}, \mathrm{W}=21 \mathrm{ft} $$.
The garden with the largest area is $$ \mathrm{L}=21 \mathrm{ft}, \mathrm{W}=21 \mathrm{ft} $$.

Multiple Choice 1 point

Greg is making a rectangular garden. He has purchased 84 feet of fencing.
What length and width will maximize the area of a garden with a perimeter of 84 feet?
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Multiple Choice 1 point Greg is making a rectangular garden. He has purchased 84 feet of fencing. What length and width will maximize the area of a garden with a perimeter of 84 feet? . . . .