Solving Systems of Non-Linear Equations Using Perimeter and Area Formulas

This lesson teaches how to write and solve systems of non-linear equations using area and perimeter formulas for rectangles. It reviews rectangle basics, including dimensions, area, and perimeter. The lesson demonstrates solving for the dimensions of a rectangular cornfield with given perimeter and area, using substitution to create a quadratic equation. A similar problem is explored, showing how different parameters can lead to non-real solutions. The lesson concludes with a recap of the key concepts and methods used.

What is the formula for the perimeter of a rectangle?

• Length minus width

• Length multiplied by width

• Length plus width

• 2 times the length plus 2 times the width

In the example problem, what is the perimeter of the cornfield?

• 345 yards

• 690 yards

• 27,000 yards

• 120 yards

What method can be used to solve the quadratic equation in the example problem?

• By factoring, graphing, completing the square, or the quadratic formula

• Only by graphing

• Only by the quadratic formula

• Only by completing the square

What are the possible values for the width in the first example problem?

• 120 or 225

• 80 or 160

• 345 or 690

• 160 or 3500

Why is the solution in the second example not valid?

• The numbers are too large

• The numbers are not real

• The numbers are negative

• The numbers are imaginary