Rectangle Dimensions and Properties

The video tutorial explains how to find the dimensions of a rectangle given its area and perimeter. It starts by introducing the problem and formulating two equations based on the area and perimeter formulas. The tutorial then demonstrates solving these equations using the substitution method, leading to a quadratic equation. By factoring the quadratic equation, the dimensions of the rectangle are determined to be 11 cm by 16 cm.

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

• 176 cm squared

• 54 cm squared

• 100 cm squared

• 200 cm squared

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

• 100 cm

• 54 cm

• 200 cm

• 176 cm

Which formula is used to calculate the area of a rectangle?

• 2 x (Length + Width)

• Length + Width

• Length - Width

• Length x Width

What is the first equation derived from the area of the rectangle?

• 176 = Length + Width

• 176 = Length x Width

• 176 = 2 x (Length + Width)

• 176 = Length - Width

What is the formula for the perimeter of a rectangle?

• Length x Width

• 2 x (Length + Width)

• Length + Width

• Length - Width

What is the simplified second equation derived from the perimeter?

• 54 = Length x Width

• 54 = Length + Width

• 27 = Length x Width

• 27 = Length + Width

What method is used to solve the equations for the rectangle's dimensions?

• Completing the square

• Graphing

• Substitution

• Elimination

What expression is substituted for W in the first equation?

• 27 + L

• 27 - L

• L - 27

• L + 27

What type of equation is formed after substitution?

• Linear equation

• Quadratic equation

• Cubic equation

• Exponential equation

What are the factors of the quadratic equation derived from the problem?

• 11 and 16

• 10 and 17

• 8 and 22

• 12 and 14