Maximizing the Area of a Rectangular Garden

The video tutorial explains how a rancher can use 300 yards of fencing to enclose three sides of a rectangular garden, with the fourth side being a cliff. The goal is to find the dimensions that maximize the garden's area. The tutorial defines variables for width and length, sets up a constraint equation, and derives an area equation in terms of one variable. It explains quadratic functions and how to find the vertex, which gives the maximum area. Finally, it calculates the dimensions of the garden that provide the largest area.

What is the total length of fencing available to the rancher?

• 400 yards

• 300 yards

• 500 yards

• 200 yards

Which side of the garden does not require fencing?

• West side

• Cliff side

• East side

• North side

What is the constraint equation for the fencing problem?

• 2l + 2w = 300

• l + w = 300

• l + 2w = 300

• 2l + w = 300

How is the area of the garden expressed in terms of width (w)?

• w^2 + 300w

• 2w + 300

• 300 - 2w

• 300w - 2w^2

What type of function is used to represent the area of the garden?

• Quadratic

• Linear

• Exponential

• Logarithmic

What is the significance of the vertex in the quadratic function for this problem?

• It gives the average area

• It gives the maximum area

• It gives the total area

• It gives the minimum area

What is the width of the garden that maximizes the area?

• 150 yards

• 50 yards

• 75 yards

• 100 yards

What is the maximum area of the garden?

• 15,000 square yards

• 12,500 square yards

• 10,000 square yards

• 11,250 square yards

How is the length of the garden calculated once the width is known?

• l = 300 - w

• l = 300 - 2w

• l = w + 300

• l = 2w - 300

What is the length of the garden that maximizes the area?

• 100 yards

• 175 yards

• 150 yards

• 125 yards