Rectangle Dimensions and Area Problems

The video tutorial explains how to find the width and length of a rectangle given that its length is 3 inches more than its width and its area is 130 square inches. The process involves setting up a quadratic equation using the area formula, solving it by factoring, and validating the solution to ensure positive dimensions. The final solution reveals the width as 10 inches and the length as 13 inches, confirming the area and the condition that the length is 3 inches more than the width.

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

• The length is equal to the width.

• The length is 3 inches more than the width.

• The length is twice the width.

• The width is 3 inches more than the length.

What is the area of the rectangle?

• 130 square inches

• 100 square inches

• 120 square inches

• 150 square inches

How is the length expressed in terms of the width?

• Length = Width + 3

• Length = Width * 3

• Length = Width - 3

• Length = Width + 5

What equation is formed using the area formula?

• x^2 + 3x - 130 = 0

• x^2 + 3x = 130

• x^2 - 3x - 130 = 0

• x^2 - 3x = 130

What are the factors of the quadratic equation?

• (x + 10)(x + 13)

• (x - 10)(x - 13)

• (x + 13)(x - 10)

• (x + 10)(x - 13)

What is the value of x that represents the width?

• x = 13

• x = -13

• x = 10

• x = -10

Why is x = -13 not a valid solution?

• Because it makes the width negative.

• Because it makes the equation unsolvable.

• Because it makes the length negative.

• Because it makes the area negative.

What is the length of the rectangle?

• 15 inches

• 12 inches

• 13 inches

• 10 inches

What is the width of the rectangle?

• 15 inches

• 13 inches

• 10 inches

• 12 inches

What is the product of the length and width of the rectangle?

• 130 square inches

• 150 square inches

• 140 square inches

• 120 square inches