Solving Nonlinear Equations for Rectangle Dimensions

The video tutorial explains how to find the dimensions of a rectangle given its area and perimeter. It starts by setting up equations for the area and perimeter, then uses substitution to solve the system of equations. The quadratic equation is factored to find possible values for the rectangle's dimensions. The tutorial concludes by confirming the dimensions and summarizing the solution process.

What is the area of the rectangle?

• 176 square centimeters

• 54 square centimeters

• 88 square centimeters

• 27 square centimeters

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CCSS.8.EE.C.7B

What formula represents the perimeter of the rectangle?

• 2(x + y)

• x + y

• x * y

• 2x + 2y

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CCSS.4.MD.A.3

What is the perimeter of the rectangle?

• 54 centimeters

• 176 centimeters

• 27 centimeters

• 88 centimeters

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CCSS.4.MD.A.3

CCSS.3.MD.C.7B

What equation is used to calculate the area of the rectangle?

• Length times width

• 2 times (length + width)

• Length plus width

• Length minus width

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CCSS.6.EE.C.9

How is 'y' expressed in terms of 'x'?

• 27 - x

• x - 27

• 54 - 2x

• 2x - 54

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CCSS.8.EE.C.8C

How do you solve the system of equations to find the rectangle's dimensions?

• Using matrices

• Graphically

• Using elimination

• Using substitution

What type of equation is formed when substituting 'y' in the area formula?

• Exponential equation

• Cubic equation

• Linear equation

• Quadratic equation

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CCSS.HSA-REI.B.4B

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

• -8 and -22

• 16 and 11

• 8 and 22

• -16 and -11

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CCSS.HSA-REI.B.4B

Which step involves breaking down 176 into its prime factors?

• Solving for 'y'

• Setting up the area equation

• Determining the perimeter

• Factoring the quadratic equation

Tags

CCSS.8.EE.A.2

What are the dimensions of the rectangle?

• 54 cm by 54 cm

• 27 cm by 27 cm

• 11 cm by 16 cm

• 16 cm by 11 cm

Tags

CCSS.8.EE.A.2