Rectangle Dimensions and Properties

The video tutorial explains how to find the dimensions of a rectangle given its area and perimeter. It starts by labeling the sides of the rectangle and formulating equations for area and perimeter. The tutorial then demonstrates solving these equations using substitution and factoring a quadratic equation. Finally, it determines the dimensions of the rectangle, ensuring they match the given area and perimeter.

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

• 176 square centimeters

• 200 square centimeters

• 54 square centimeters

• 100 square centimeters

What equation represents the perimeter of the rectangle?

• X * Y = 54

• X + Y = 54

• X - Y = 54

• 2X + 2Y = 54

What is the first step in solving the system of equations using substitution?

• Divide both sides by 2

• Multiply both sides by 2

• Add 2X to both sides

• Subtract 2X from both sides

What is the quadratic equation obtained after substitution?

• X^2 - 176X + 27 = 0

• X^2 - 27X + 176 = 0

• X^2 + 27X - 176 = 0

• X^2 + 176X - 27 = 0

What are the factors of 176 that add up to -27?

• 16 and 11

• -16 and -11

• 8 and 19

• -8 and -19

What are the possible values for X after solving the quadratic equation?

• X = 27 or X = 16

• X = 16 or X = 11

• X = 11 or X = 27

• X = 16 or X = 27

If X is 16, what is the value of Y?

• Y = 54

• Y = 27

• Y = 11

• Y = 16

What are the final dimensions of the rectangle?

• 16 cm by 11 cm

• 11 cm by 16 cm

• 27 cm by 16 cm

• 16 cm by 27 cm

What is the perimeter of the rectangle with the final dimensions?

• 32 centimeters

• 27 centimeters

• 176 centimeters

• 54 centimeters

What method was used to solve the system of equations?

• Matrix

• Substitution

• Elimination

• Graphing