Rectangle Perimeter and Area Problems

The video tutorial explains how to find the dimensions of a rectangle given its perimeter and area. It starts by modeling the problem using variables for the rectangle's sides, then sets up equations for the perimeter and area. The tutorial demonstrates solving these equations using substitution and factoring a quadratic equation. Finally, it identifies the rectangle's dimensions and concludes with the solution.

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

• 23 cm

• 10 cm

• 130 cm

• 46 cm

What equation represents the perimeter of the rectangle?

• x * y = 130

• 2x + 2y = 46

• x^2 + y^2 = 46

• x + y = 46

Which method is used to solve the system of equations in the video?

• Graphing

• Elimination

• Matrix

• Substitution

What is the expression for y after isolating it in the perimeter equation?

• y = 46 - 2x

• y = x + 23

• y = 2x - 46

• y = 23 - x

What type of equation is formed after substituting y in the area equation?

• Linear equation

• Quadratic equation

• Cubic equation

• Exponential equation

What are the factors of the quadratic equation x^2 - 23x + 130?

• (x - 10)(x + 13)

• (x + 13)(x + 10)

• (x - 13)(x - 10)

• (x + 10)(x - 13)

What are the possible values of x after solving the quadratic equation?

• x = 23 or x = 130

• x = 10 or x = 13

• x = 13 or x = 23

• x = 10 or x = 23

If x is 13, what is the value of y?

• 23

• 13

• 10

• 46

What are the final dimensions of the rectangle?

• 10 cm x 13 cm

• 13 cm x 23 cm

• 23 cm x 46 cm

• 10 cm x 23 cm

Which side of the rectangle is considered the short side?

• 10 cm

• 13 cm

• 23 cm

• 46 cm