Question

tyler is building a pen for his rabbit on the side of the garage. he needs to fence in three sides and wants to use 24 ft of fencing.

1. the table shows some possible lengths and widths. complete each area.
2. which length and width combination should tyler choose to give his rabbit the most room?

length (ft)	width (ft)	area (sq ft)
10	7
12	6
14	5
16	4

Explanation:

Part 1: Completing the Area Table

To find the area of a rectangle, we use the formula \( \text{Area} = \text{length} \times \text{width} \). Let's calculate the area for each row:

Row 1: Length = 8 ft, Width = 8 ft

Step 1: Apply the area formula

The formula for the area of a rectangle is \( A = l \times w \), where \( l \) is the length and \( w \) is the width.
Substitute \( l = 8 \) and \( w = 8 \) into the formula:
\( A = 8 \times 8 = 64 \) square feet.

Row 2: Length = 10 ft, Width = 7 ft

Step 1: Apply the area formula

Substitute \( l = 10 \) and \( w = 7 \) into \( A = l \times w \):
\( A = 10 \times 7 = 70 \) square feet.

Row 3: Length = 12 ft, Width = 6 ft

Step 1: Apply the area formula

Substitute \( l = 12 \) and \( w = 6 \) into \( A = l \times w \):
\( A = 12 \times 6 = 72 \) square feet.

Row 4: Length = 14 ft, Width = 5 ft

Step 1: Apply the area formula

Substitute \( l = 14 \) and \( w = 5 \) into \( A = l \times w \):
\( A = 14 \times 5 = 70 \) square feet.

Row 5: Length = 16 ft, Width = 4 ft

Step 1: Apply the area formula

Substitute \( l = 16 \) and \( w = 4 \) into \( A = l \times w \):
\( A = 16 \times 4 = 64 \) square feet.

The completed table is:

length (ft)	width (ft)	area (sq ft)
10	7	70
12	6	72
14	5	70
16	4	64

Part 2: Finding the Combination with the Most Room

To determine which length and width combination gives the most room (largest area), we compare the areas calculated in Part 1:

• For length = 8 ft, width = 8 ft: Area = 64 sq ft
• For length = 10 ft, width = 7 ft: Area = 70 sq ft
• For length = 12 ft, width = 6 ft: Area = 72 sq ft
• For length = 14 ft, width = 5 ft: Area = 70 sq ft
• For length = 16 ft, width = 4 ft: Area = 64 sq ft

Among these areas, 72 square feet is the largest, which corresponds to a length of 12 ft and a width of 6 ft.

Final Answers

Part 1:

length (ft)	width (ft)	area (sq ft)
10	7	70
12	6	72
14	5	70
16	4	64

Part 2:

Tyler should choose a length of 12 ft and a width of 6 ft to give his rabbit the most room.

Answer:

Part 1: Completing the Area Table

To find the area of a rectangle, we use the formula \( \text{Area} = \text{length} \times \text{width} \). Let's calculate the area for each row:

Row 1: Length = 8 ft, Width = 8 ft

Step 1: Apply the area formula

The formula for the area of a rectangle is \( A = l \times w \), where \( l \) is the length and \( w \) is the width.
Substitute \( l = 8 \) and \( w = 8 \) into the formula:
\( A = 8 \times 8 = 64 \) square feet.

Row 2: Length = 10 ft, Width = 7 ft

Step 1: Apply the area formula

Substitute \( l = 10 \) and \( w = 7 \) into \( A = l \times w \):
\( A = 10 \times 7 = 70 \) square feet.

Row 3: Length = 12 ft, Width = 6 ft

Step 1: Apply the area formula

Substitute \( l = 12 \) and \( w = 6 \) into \( A = l \times w \):
\( A = 12 \times 6 = 72 \) square feet.

Row 4: Length = 14 ft, Width = 5 ft

Step 1: Apply the area formula

Substitute \( l = 14 \) and \( w = 5 \) into \( A = l \times w \):
\( A = 14 \times 5 = 70 \) square feet.

Row 5: Length = 16 ft, Width = 4 ft

Step 1: Apply the area formula

Substitute \( l = 16 \) and \( w = 4 \) into \( A = l \times w \):
\( A = 16 \times 4 = 64 \) square feet.

The completed table is:

length (ft)	width (ft)	area (sq ft)
10	7	70
12	6	72
14	5	70
16	4	64

Part 2: Finding the Combination with the Most Room

To determine which length and width combination gives the most room (largest area), we compare the areas calculated in Part 1:

• For length = 8 ft, width = 8 ft: Area = 64 sq ft
• For length = 10 ft, width = 7 ft: Area = 70 sq ft
• For length = 12 ft, width = 6 ft: Area = 72 sq ft
• For length = 14 ft, width = 5 ft: Area = 70 sq ft
• For length = 16 ft, width = 4 ft: Area = 64 sq ft

Among these areas, 72 square feet is the largest, which corresponds to a length of 12 ft and a width of 6 ft.

Final Answers

Part 1:

length (ft)	width (ft)	area (sq ft)
10	7	70
12	6	72
14	5	70
16	4	64

Part 2:

Tyler should choose a length of 12 ft and a width of 6 ft to give his rabbit the most room.