Question

1. complete a table of values for the width and length of a rectangle with an area of 12 square inches. then complete the graph.

table: width of rectangle (in.) with values 1, 6, (blank), (blank), (blank), 20; length of rectangle (in.) with values (blank), (blank), 3, 8, 0.75 (3/4), (blank). graph: y-axis (length (inches)), x-axis (width (inches))

1. describe how the width of the rectangle affects the length of the rectangle.
2. do the width...

Explanation:

Question 6: Completing the Table

The area \( A \) of a rectangle is given by \( A = \text{width} \times \text{length} \). Here, \( A = 12 \) square inches, so \( \text{length} = \frac{12}{\text{width}} \) and \( \text{width} = \frac{12}{\text{length}} \).

Step 1: Width = 1 inch

Use \( \text{length} = \frac{12}{\text{width}} \).
\( \text{length} = \frac{12}{1} = 12 \) inches.

Step 2: Width = 6 inches

\( \text{length} = \frac{12}{6} = 2 \) inches.

Step 3: Length = 3 inches

Use \( \text{width} = \frac{12}{\text{length}} \).
\( \text{width} = \frac{12}{3} = 4 \) inches.

Step 4: Length = 8 inches

\( \text{width} = \frac{12}{8} = 1.5 \) inches (or \( \frac{3}{2} \) inches).

Step 5: Length = 0.75 inches

\( \text{width} = \frac{12}{0.75} = 16 \) inches.

Step 6: Width = 20 inches

\( \text{length} = \frac{12}{20} = 0.6 \) inches.

Filled Table:

Width (in.)	Length (in.)
6	2
4	3
1.5	8
16	0.75
20	0.6

Question 7: Relationship Between Width and Length

The area of the rectangle is constant (\( 12 \) square inches). From the formula \( \text{length} = \frac{12}{\text{width}} \), length and width are inversely proportional. As the width of the rectangle increases, the length decreases (and vice versa), because their product (the area) remains fixed at 12.

Final Answers (Table for Q6):

Width (in.)	Length (in.)
6	2
4	3
1.5	8
16	0.75
20	0.6

(For the graph, plot the points \((1, 12)\), \((6, 2)\), \((4, 3)\), \((1.5, 8)\), \((16, 0.75)\), \((20, 0.6)\) with width on the x - axis and length on the y - axis.)

For Q7: The width and length of the rectangle are inversely proportional. As the width increases, the length decreases (and as the width decreases, the length increases) because their product (the area of the rectangle) is a constant (12 square inches).

Answer:

Question 6: Completing the Table

The area \( A \) of a rectangle is given by \( A = \text{width} \times \text{length} \). Here, \( A = 12 \) square inches, so \( \text{length} = \frac{12}{\text{width}} \) and \( \text{width} = \frac{12}{\text{length}} \).

Step 1: Width = 1 inch

Use \( \text{length} = \frac{12}{\text{width}} \).
\( \text{length} = \frac{12}{1} = 12 \) inches.

Step 2: Width = 6 inches

\( \text{length} = \frac{12}{6} = 2 \) inches.

Step 3: Length = 3 inches

Use \( \text{width} = \frac{12}{\text{length}} \).
\( \text{width} = \frac{12}{3} = 4 \) inches.

Step 4: Length = 8 inches

\( \text{width} = \frac{12}{8} = 1.5 \) inches (or \( \frac{3}{2} \) inches).

Step 5: Length = 0.75 inches

\( \text{width} = \frac{12}{0.75} = 16 \) inches.

Step 6: Width = 20 inches

\( \text{length} = \frac{12}{20} = 0.6 \) inches.

Filled Table:

Width (in.)	Length (in.)
6	2
4	3
1.5	8
16	0.75
20	0.6

Question 7: Relationship Between Width and Length

The area of the rectangle is constant (\( 12 \) square inches). From the formula \( \text{length} = \frac{12}{\text{width}} \), length and width are inversely proportional. As the width of the rectangle increases, the length decreases (and vice versa), because their product (the area) remains fixed at 12.

Final Answers (Table for Q6):

Width (in.)	Length (in.)
6	2
4	3
1.5	8
16	0.75
20	0.6

(For the graph, plot the points \((1, 12)\), \((6, 2)\), \((4, 3)\), \((1.5, 8)\), \((16, 0.75)\), \((20, 0.6)\) with width on the x - axis and length on the y - axis.)

For Q7: The width and length of the rectangle are inversely proportional. As the width increases, the length decreases (and as the width decreases, the length increases) because their product (the area of the rectangle) is a constant (12 square inches).