Quadratics in Area & Perimeter: Solve & Graph Functions

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? Use the quadratic formula to find the width.

• Width: 8 meters, Length: 11 meters

• Width: 6 meters, Length: 9 meters

• Width: 7 meters, Length: 10 meters

• Width: 5 meters, Length: 8 meters

A square park has a perimeter of 64 meters. If the park is expanded by increasing each side by a certain number of meters, express the new area as a quadratic function of the side length increase. What is the new area if each side is increased by 2 meters?

• 400 square meters

• 256 square meters

• 144 square meters

• 324 square meters

A rectangular swimming pool has a length that is twice its width. If the perimeter of the pool is 60 meters, find the dimensions of the pool using a quadratic equation.

• Width: 15 meters, Length: 30 meters

• Width: 12 meters, Length: 24 meters

• Width: 5 meters, Length: 10 meters

• Width: 10 meters, Length: 20 meters

The area of a triangular field is given by the formula A = 1/2 * base * height. If the base is 4 meters longer than the height and the area is 48 square meters, find the dimensions of the field using the quadratic formula.

• Height: 8 meters, Base: 12 meters

• Height: 5 meters, Base: 9 meters

• Height: 6 meters, Base: 10 meters

• Height: 10 meters, Base: 14 meters

A rectangular plot of land has a length that is 5 meters more than its width. If the area of the plot is 150 square meters, find the dimensions of the plot by graphing the quadratic function derived from the area formula.

• Width: 5 meters, Length: 10 meters

• Width: 12 meters, Length: 17 meters

• Width: 8 meters, Length: 13 meters

• Width: 10 meters, Length: 15 meters

A farmer wants to create a rectangular fence with a perimeter of 100 meters. If the length is represented as x and the width as (50 - x), write a quadratic equation for the area and find the maximum area using the vertex form of the quadratic function.

• 750 square meters

• 500 square meters

• 625 square meters

• 400 square meters

A rectangular room has a length that is 4 feet longer than its width. If the area of the room is 60 square feet, find the dimensions of the room using the quadratic formula.

• Width: 8 feet, Length: 12 feet

• Width: 5 feet, Length: 9 feet

• Width: 7 feet, Length: 11 feet

• Width: 6 feet, Length: 10 feet

A rectangular garden has a width of x meters and a length of (x + 6) meters. If the area of the garden is 72 square meters, set up a quadratic equation and solve for x to find the dimensions of the garden.

• Width: 4 meters, Length: 16 meters

• Width: 8 meters, Length: 10 meters

• Width: 10 meters, Length: 18 meters

• Width: 6 meters, Length: 12 meters

A rectangular field has a length that is 3 meters less than twice its width. If the perimeter of the field is 54 meters, find the dimensions of the field using a quadratic equation.

• Width: 9 meters, Length: 15 meters

• Width: 12 meters, Length: 21 meters

• Width: 8 meters, Length: 13 meters

• Width: 10 meters, Length: 17 meters

A rectangular box has a length that is 3 inches longer than its width. If the volume of the box is 120 cubic inches and the height is 5 inches, find the dimensions of the box using the quadratic formula.

• Width: 3 inches, Length: 6 inches, Height: 5 inches

• Width: 6 inches, Length: 9 inches, Height: 5 inches

• Width: 5 inches, Length: 8 inches, Height: 5 inches

• Width: 4 inches, Length: 7 inches, Height: 5 inches