Maximizing Area: Quadratic Functions in Rectangles

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 70 square meters, what are the dimensions of the garden?

• Width: 7 meters, Length: 10 meters

• Width: 8 meters, Length: 11 meters

• Width: 6 meters, Length: 9 meters

• Width: 5 meters, Length: 8 meters

The area of a rectangular swimming pool is represented by the equation A = x(10 - x), where x is the width in meters. What is the maximum area of the pool, and what are the dimensions when the area is maximized?

• Maximum area is 25 square meters with dimensions 5m x 5m.

• Maximum area is 15 square meters with dimensions 3m x 5m.

• Maximum area is 30 square meters with dimensions 6m x 5m.

• Maximum area is 20 square meters with dimensions 4m x 5m.

A rectangular field has a perimeter of 60 meters. If the length is represented as x and the width as (30 - x), write a quadratic equation for the area of the field and find the dimensions that maximize the area.

• Length: 10 meters, Width: 20 meters

• Length: 20 meters, Width: 10 meters

• Length: 15 meters, Width: 15 meters

• Length: 25 meters, Width: 5 meters

A rectangular poster has a width that is 4 inches less than its length. If the area of the poster is 96 square inches, what are the dimensions of the poster?

• 14 inches by 10 inches

• 10 inches by 6 inches

• 12 inches by 8 inches

• 8 inches by 4 inches

The length of a rectangular box is twice its width. If the volume of the box is 128 cubic inches, express the volume as a quadratic equation and find the dimensions of the box.

• Width: 4 inches, Length: 8 inches, Height: 4 inches

• Width: 10 inches, Length: 20 inches, Height: 0.5 inches

• Width: 6 inches, Length: 12 inches, Height: 2 inches

• Width: 8 inches, Length: 16 inches, Height: 1 inch

A rectangular plot of land has a length that is 5 meters more than its width. If the area of the plot is 100 square meters, find the dimensions of the plot and graph the quadratic function representing the area.

• Width: 10 meters, Length: 15 meters

• Width: 12 meters, Length: 17 meters

• Width: 5 meters, Length: 10 meters

• Width: 8 meters, Length: 13 meters

A rectangular garden's length is 2 meters less than three times its width. If the area of the garden is 50 square meters, determine the dimensions of the garden and sketch the graph of the area as a function of width.

• Width: 6 meters, Length: 12 meters

• Width: 5 meters, Length: 15 meters

• Width: 4 meters, Length: 10 meters

• Width: 5 meters, Length: 13 meters

The width of a rectangular room is 2 feet less than its length. If the area of the room is 48 square feet, write a quadratic equation to represent the area and find the dimensions of the room.

• Length: 6 feet, Width: 8 feet

• Length: 10 feet, Width: 4 feet

• Length: 7 feet, Width: 5 feet

• Length: 8 feet, Width: 6 feet

A rectangular fence is to be built around a garden. If the length is 4 meters more than the width and the total area enclosed is 96 square meters, find the dimensions of the garden and graph the quadratic function for the area.

• Width: 5 meters, Length: 9 meters

• Width: 10 meters, Length: 14 meters

• Width: 6 meters, Length: 10 meters

• Width: 8 meters, Length: 12 meters