Understanding the Frame Problem

The video tutorial explains how to determine the width of a frame surrounding a sketch. The sketch is a 6x9 inch rectangle, and the frame has a uniform width. The area of the sketch equals the area of the frame. The tutorial guides viewers through calculating the area of the sketch, setting up an equation for the total area, and solving a quadratic equation to find the frame's width. The solution reveals that the frame's width is 1.5 inches.

What are the dimensions of the sketch placed in the frame?

• 7 in by 10 in

• 6 in by 9 in

• 5 in by 8 in

• 8 in by 11 in

If the area of the sketch is 54 square inches, what is the area of the frame?

• 27 square inches

• 54 square inches

• 81 square inches

• 108 square inches

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

• w

• x

• z

• y

What is the total area of the larger rectangle, including both the sketch and the frame?

• 162 square inches

• 54 square inches

• 72 square inches

• 108 square inches

Which of the following is the correct expression for the area of the larger rectangle?

• (9 + 3x) * (6 + 3x)

• (9 + 2x) * (6 + 2x)

• (9 + x) * (6 + x)

• (9 + x) * (6 + 2x)

What is the first step in solving the quadratic equation obtained from the area expression?

• Divide both sides by 2

• Multiply both sides by 2

• Subtract 108 from both sides

• Add 108 to both sides

What is the greatest common factor factored out from the quadratic equation?

• 2

• 3

• 1

• 4

Which pair of factors is used to factor the trinomial inside the parentheses?

• 4x and x

• 3x and x

• 2x and x

• 5x and x

What is the correct width of the frame?

• 2 inches

• 1.5 inches

• 2.5 inches

• 1 inch

Why is the negative solution for x discarded?

• It is not a real number

• It does not satisfy the equation

• It represents a negative length

• It is greater than the frame's length