Quadratic Dimensions: Area, Vertex, and Symmetry Challenge

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: 5 meters, Length: 8 meters

• Width: 8 meters, Length: 11 meters

• Width: 7 meters, Length: 10 meters

• Width: 6 meters, Length: 9 meters

A triangular park has a base that is 4 meters longer than its height. If the area of the park is 48 square meters, determine the height and base of the park using the quadratic formula.

• Height: 8 meters, Base: 12 meters

• Height: 10 meters, Base: 14 meters

• Height: 6 meters, Base: 10 meters

• Height: 4 meters, Base: 8 meters

A rectangular swimming pool has a length that is twice its width. If the area of the pool is 200 square meters, find the dimensions of the pool and identify the vertex of the quadratic equation formed.

• Width: 15 meters, Length: 30 meters

• Width: 5 meters, Length: 10 meters

• Width: 8 meters, Length: 16 meters

• Width: 10 meters, Length: 20 meters

A farmer wants to create a rectangular field with an area of 1200 square meters. If the length is 10 meters more than the width, find the dimensions of the field and determine the axis of symmetry of the quadratic equation.

• Width: 30 meters, Length: 40 meters; Axis of symmetry: -5.

• Width: 35 meters, Length: 45 meters; Axis of symmetry: -2.5.

• Width: 25 meters, Length: 35 meters; Axis of symmetry: -7.5.

• Width: 20 meters, Length: 30 meters; Axis of symmetry: -10.

A square plot of land has an area represented by the equation x^2 = 64. What is the length of each side, and what is the vertex of the quadratic function representing the area?

• Length of each side: 6 units; Vertex: (0, 0)

• Length of each side: 8 units; Vertex: (0, 0)

• Length of each side: 8 units; Vertex: (2, 2)

• Length of each side: 10 units; Vertex: (0, 64)

A rectangular room has a length that is 5 feet longer than its width. If the area of the room is 60 square feet, find the dimensions of the room and identify the axis of symmetry of the quadratic equation.

• Dimensions: 3 feet (width) and 8 feet (length); Axis of symmetry: x = -1.5

• Dimensions: 6 feet (width) and 11 feet (length); Axis of symmetry: x = -3.5

• Dimensions: 5 feet (width) and 10 feet (length); Axis of symmetry: x = -2.5

• Dimensions: 4 feet (width) and 9 feet (length); Axis of symmetry: x = -3

A rectangular box has a length that is 4 inches longer than its width. If the area of the base of the box is 96 square inches, find the dimensions of the base and apply the quadratic formula to solve for the width.

• Width: 5 inches, Length: 9 inches

• Width: 8 inches, Length: 12 inches

• Width: 6 inches, Length: 10 inches

• Width: 10 inches, Length: 14 inches

A garden is designed in the shape of a rectangle where the length is 2 meters less than three times the width. If the area of the garden is 50 square meters, find the dimensions and the vertex of the quadratic equation.

• Width: 5 meters, Length: 13 meters, Vertex: (1/3, -169/12)

• Width: 7 meters, Length: 14 meters, Vertex: (1/2, -200/12)

• Width: 6 meters, Length: 12 meters, Vertex: (0, -144/12)

• Width: 4 meters, Length: 10 meters, Vertex: (2/3, -100/12)

A rectangular field has a width that is 6 meters less than its length. If the area of the field is 72 square meters, determine the dimensions of the field and find the axis of symmetry of the quadratic equation.

• Length: 14 meters, Width: 8 meters; Axis of symmetry: L = 7

• Length: 9 meters, Width: 3 meters; Axis of symmetry: L = 2.5

• Length: 10 meters, Width: 8 meters; Axis of symmetry: L = 4

• Length: 12 meters, Width: 6 meters; Axis of symmetry: L = 3

A rectangular painting has a length that is 3 inches longer than its width. If the area of the painting is 54 square inches, find the dimensions of the painting and apply the quadratic formula to find the width.

• Width: 4 inches, Length: 7 inches

• Width: 6 inches, Length: 9 inches

• Width: 7 inches, Length: 10 inches

• Width: 5 inches, Length: 8 inches