Carpet and Box Dimensions Problems

The video tutorial covers quadratic applications, including solving problems related to rectangles, cereal boxes, kite flying, and rug dimensions. It demonstrates the use of quadratic equations, the quadratic formula, and the Pythagorean theorem to find dimensions and solve real-world problems.

What is the relationship between the area and perimeter of the rectangle in the problem?

• The area is half the perimeter.

• The area is twice the perimeter.

• The area is equal to the perimeter.

• The area is three times the perimeter.

If the length of the rectangle is twice the width, what equation represents the perimeter?

• P = L + W

• P = 2L + 2W

• P = L + 2W

• P = 2L + W

What is the first step in solving the quadratic equation for the rectangle problem?

• Use the quadratic formula.

• Complete the square.

• Factor the equation.

• Graph the equation.

What are the dimensions of the rectangle if the width is 6?

• Length = 6, Width = 12

• Length = 10, Width = 5

• Length = 8, Width = 4

• Length = 12, Width = 6

What is the volume of the cereal box in the problem?

• 180.4 cubic inches

• 200 cubic inches

• 150 cubic inches

• 175 cubic inches

How is the length of the cereal box related to its height?

• The length is twice the height.

• The length is equal to the height.

• The length is 3.2 inches less than the height.

• The length is 3.2 inches more than the height.

Which method is used to solve the quadratic equation for the cereal box problem?

• Graphing

• Factoring

• Completing the square

• Quadratic formula

What is the height of the cereal box to the nearest tenth?

• 8.7 inches

• 10.6 inches

• 9.5 inches

• 11.2 inches

What is the length of the cereal box if the height is 10.6 inches?

• 7.4 inches

• 6.4 inches

• 8.4 inches

• 9.4 inches

How long is the string of the kite in the problem?

• 40 feet

• 50 feet

• 70 feet

• 60 feet