Room Dimensions and Area Problems

This video tutorial demonstrates solving a quadratic equation application involving the area of a rectangular living room. The problem states that the room's area is 320 square feet, with the length being four feet more than the width. The instructor sets up the equation using a diagram and solves it algebraically by factoring. The solution reveals the room's width as 16 feet and the length as 20 feet.

What is the area of the couple's living room?

• 320 square feet

• 300 square feet

• 350 square feet

• 400 square feet

How is the length of the room related to its width?

• It is twice the width

• It is four feet more than the width

• It is half the width

• It is equal to the width

What variable is used to represent the width of the room?

• x

• z

• w

• y

What equation represents the area of the room in terms of x?

• x + 4 = 320

• x(x + 4) = 320

• x^2 + 4 = 320

• x^2 = 320

What is the standard form of the quadratic equation derived from the problem?

• x^2 + 4x - 320 = 0

• x^2 - 4x = 320

• x^2 - 4x - 320 = 0

• x^2 + 4x = 320

Which method is used to solve the quadratic equation in the video?

• Completing the square

• Quadratic formula

• Factoring

• Graphing

What are the factors of 320 that are used in the solution?

• 4 and 80

• 8 and 40

• 16 and 20

• 10 and 32

What are the possible solutions for x after factoring?

• x = 16 or x = -20

• x = 20 or x = -16

• x = -16 or x = -20

• x = 16 or x = 20

What is the purpose of setting the equation to zero?

• To check for errors

• To eliminate variables

• To find the roots of the equation

• To simplify the equation

What is the significance of the positive sign in the factors?

• It ensures the larger factor is positive

• It indicates a positive area

• It balances the equation

• It shows the equation is correct