Solving Area and Perimeter Problems with Quadratics

The video tutorial covers solving problems related to the perimeter and area of rectangles. It begins with a problem involving a concrete slab, using equations to find the length of the longer side. The tutorial then moves to solving quadratic equations for a rectangle with a width less than its length. Finally, it addresses a problem involving two ranchers claiming different efficiencies in fencing rectangular pastures, using mathematical analysis to determine the truth. The video emphasizes the use of equations and quadratic solutions in solving these problems.

What is the formula for the perimeter of a rectangle?

• Perimeter = length + width

• Perimeter = 2 * (length + width)

• Perimeter = length * width

• Perimeter = 2 * length + width

How do you express width if the perimeter and length are known?

• Width = (Perimeter - 2 * length) / 2

• Width = Perimeter / 2 * length

• Width = Perimeter - length

• Width = (Perimeter + 2 * length) / 2

What type of equation is formed when substituting the expression for width into the area formula?

• Linear equation

• Cubic equation

• Exponential equation

• Quadratic equation

What are the possible values of length from the quadratic equation derived from the area and perimeter conditions?

• 35 and 20

• 28 and 13

• 30 and 15

• 25 and 10

In the second problem, what is the area of the rectangle?

• 99 square inches

• 100 square inches

• 98 square inches

• 95 square inches

What is the correct width of the rectangle in the second problem?

• 10 inches

• 11 inches

• 8 inches

• 9 inches

Which rancher's claim about the area fenced is possible?

• Susan's claim

• Bob's claim

• Both are possible

• Neither are possible

What is the maximum area that can be fenced with 440 feet of fencing?

• 12,100 square feet

• 12,400 square feet

• 12,000 square feet

• 12,500 square feet

How is the most efficient fencing area determined?

• By doubling the length of the fence

• By using the least amount of fencing material

• By making the fence circular

• By configuring the fence into a square

What is the name of the school where the teacher works?

• Virtual Learning Academy

• Minnesota Online High School

• Ed Visions Off Campus

• Internet-based School of Minnesota