Understanding the Area of a Rectangle

The video tutorial explains how to find the length and width of a rectangle given its area. The length is expressed as x + 5 and the width as x - 2. By setting up and solving a quadratic equation, the value of x is determined. The solution is used to calculate the rectangle's dimensions, ensuring they are positive. The length is found to be 14 units and the width 7 units.

What is the area of the rectangle given in the problem?

• 98 square units

• 100 square units

• 95 square units

• 90 square units

What expression represents the length of the rectangle?

• x + 3

• x - 2

• x + 5

• x - 5

What is the expression for the width of the rectangle?

• x + 5

• x + 2

• x - 5

• x - 2

What is the equation set up to find the value of x?

• 98 = (x + 5)(x - 2)

• 98 = (x - 5)(x - 2)

• 98 = (x + 3)(x - 2)

• 98 = (x + 5)(x + 2)

What is the simplified form of the equation after expanding the binomials?

• x^2 - 5x + 10

• x^2 + 5x - 10

• x^2 - 3x + 10

• x^2 + 3x - 10

What is the quadratic equation set to zero?

• x^2 - 5x + 108 = 0

• x^2 + 5x - 108 = 0

• x^2 - 3x + 108 = 0

• x^2 + 3x - 108 = 0

What are the factors of -108 that add up to 3?

• 18 and -6

• 6 and -18

• 9 and -12

• 12 and -9

What are the possible solutions for x from the factored equation?

• x = -9 and x = 12

• x = 9 and x = -12

• x = -12 and x = 9

• x = 12 and x = -9

Which value of x is valid for the length of the rectangle?

• x = 9

• x = 12

• x = -12

• x = -9

What are the final dimensions of the rectangle?

• Length: 7 units, Width: 14 units

• Length: 9 units, Width: 12 units

• Length: 12 units, Width: 9 units

• Length: 14 units, Width: 7 units