Maximizing Area of Rectangles

The video tutorial explains how to find the dimensions of a rectangle with a fixed perimeter of 1,760 cm that maximizes the area. It involves setting up equations for perimeter and area, solving for one variable, and using a quadratic function to find the maximum area. The solution reveals that the rectangle is a square with sides of 440 cm, resulting in a maximum area of 193,600 cm².

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

• 1,760 cm

• 1,800 cm

• 1,700 cm

• 1,750 cm

Tags

CCSS.HSA.CED.A.3

Which equation represents the perimeter of the rectangle?

• 2L + 2W = 1,760

• L + W = 1,760

• L * W = 1,760

• 2L + W = 1,760

How is the area of the rectangle expressed in terms of one variable?

• A = L * (880 - L)

• A = W * (880 - W)

• A = L + W

• A = 2L + 2W

Tags

CCSS.HSF-IF.C.7A

What shape does the graph of the area function take?

• A circle

• A straight line

• A parabola opening downwards

• A parabola opening upwards

What is the significance of the vertex in the graph of the area function?

• It represents the perimeter.

• It represents the average area.

• It represents the maximum area.

• It represents the minimum area.

What is the length of the rectangle when the area is maximized?

• 440 cm

• 660 cm

• 880 cm

• 220 cm

What is the maximum area of the rectangle?

• 19,000 cm²

• 19,500 cm²

• 19,300 cm²

• 19,600 cm²

What is the width of the rectangle when the area is maximized?

• 440 cm

• 880 cm

• 220 cm

• 660 cm

What conclusion can be drawn about the shape of the rectangle with maximum area?

• It is a trapezoid.

• It is a triangle.

• It is a circle.

• It is a square.

Why is the rectangle with maximum area a square?

• Because the area is minimized.

• Because all sides are equal.

• Because the length is twice the width.

• Because the perimeter is minimized.