Understanding Rectangles and Quadratic Equations

The video tutorial explains how to determine the original dimensions of a rectangle given that its length is 8 feet longer than its width. When each side is increased by 8 feet, the area becomes four times larger. The process involves setting up an equation based on these conditions, solving a quadratic equation, and using trial and error to factor it. The final solution reveals the original width and length of the rectangle.

What is the relationship between the length and width of the original rectangle?

• The length and width are equal.

• The length is 8 feet longer than the width.

• The length is twice the width.

• The width is 8 feet longer than the length.

What happens to the area of the rectangle when each side is increased by 8 feet?

• The area is doubled.

• The area is tripled.

• The area is multiplied by four.

• The area remains the same.

How is the area of the original rectangle expressed in terms of x?

• x * (x + 16)

• x^2 + 8x

• x * (x + 8)

• x^2 + 16x

What is the equation set up to find the original dimensions of the rectangle?

• x * (x + 16) = 4 * (x + 8)

• 4 * (x + 8) = x * (x + 16)

• x * (x + 8) = 4 * (x + 8) * (x + 16)

• 4x * (x + 8) = (x + 8) * (x + 16)

What is the first step in solving the quadratic equation?

• Add x^2 to both sides.

• Subtract x^2 from both sides.

• Multiply both sides by 4.

• Divide both sides by x.

What method is used to solve the quadratic equation in this problem?

• Trial and error

• Using the quadratic formula

• Completing the square

• Graphing

What are the factors used in the trial and error method?

• 8 and 16

• -8 and -16

• -16 and 8

• -8 and 16

What is the width of the original rectangle?

• 16/3 feet

• 8 feet

• 40/3 feet

• 24 feet

What is the length of the original rectangle?

• 24 feet

• 8 feet

• 16/3 feet

• 40/3 feet

Why is the solution x = -8 excluded?

• Because it does not satisfy the original equation.

• Because it is not a real number.

• Because it results in a negative length.

• Because it is not a factor of the equation.