Quadratic Area Challenges: Area Formulas & Graphing

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: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

• Width: 8 meters, Length: 11 meters

A rectangular swimming pool has a width of 4 meters and a length that is 2 meters longer than its width. Write a quadratic equation to represent the area of the pool and find its dimensions.

• Width: 3 meters, Length: 5 meters, Area: 15 square meters

• Width: 4 meters, Length: 6 meters, Area: 24 square meters

• Width: 4 meters, Length: 4 meters, Area: 16 square meters

• Width: 5 meters, Length: 7 meters, Area: 35 square meters

The area of a triangular park is represented by the equation A = 1/2 * base * height. If the base is represented as x and the height is x + 4, find the area when x = 6 meters.

• 36 square meters

• 24 square meters

• 30 square meters

• 18 square meters

A rectangular field's length is twice its width. If the area of the field is 200 square meters, find the dimensions of the field using a quadratic equation.

• Width: 5 meters, Length: 10 meters

• Width: 10 meters, Length: 20 meters

• Width: 12 meters, Length: 24 meters

• Width: 15 meters, Length: 30 meters

A farmer wants to create a rectangular pen for his sheep. If the length is 5 meters more than the width and the area is 60 square meters, what are the dimensions of the pen?

• Length: 12 meters, Width: 4 meters

• Length: 15 meters, Width: 10 meters

• Length: 10 meters, Width: 5 meters

• Length: 8 meters, Width: 3 meters

A rectangular plot of land has an area of 150 square meters. If the length is represented as x and the width as x - 5, find the dimensions of the plot using a quadratic equation.

• Length: 12 meters, Width: 7 meters

• Length: 15 meters, Width: 10 meters

• Length: 20 meters, Width: 5 meters

• Length: 18 meters, Width: 3 meters

A rectangular box has a length that is 4 cm longer than its width. If the volume of the box is 96 cubic centimeters, write a quadratic equation to find the dimensions of the box.

• x^2 + 2x - 96 = 0

• x^2 - 4x - 96 = 0

• x^2 + 4x - 96 = 0

• x^2 + 4x + 96 = 0

The area of a rectangular garden is given by the equation A = x(x + 3). What is the area when the width is 5 meters?

• 50 square meters

• 30 square meters

• 40 square meters

• 25 square meters

A rectangular room has a length that is 2 meters less than twice its width. If the area of the room is 48 square meters, find the dimensions of the room using a quadratic equation.

• Width: 6 meters, Length: 10 meters

• Width: 4 meters, Length: 6 meters

• Width: 3 meters, Length: 4 meters

• Width: 5 meters, Length: 8 meters

A rectangular piece of land has a length that is 6 meters longer than its width. If the area of the land is 72 square meters, write a quadratic equation to find the dimensions of the land.

• w^2 + 6w - 72 = 0

• w^2 + 6w + 72 = 0

• w^2 - 6w + 72 = 0

• w^2 - 6w - 72 = 0