Quadratic Equations in Real-Life Dimensions for Grade 9

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? Identify the quadratic equation involved.

• Width = 6 meters, Length = 9 meters

• Width = 4 meters, Length = 7 meters

• Width = 5 meters, Length = 8 meters

• Width = 7 meters, Length = 10 meters

A rectangular pool has a width of x meters and a length of (x + 5) meters. If the area of the pool is 60 square meters, write the quadratic equation to find the width of the pool.

• x^2 + 5x + 60 = 0

• x^2 - 5x + 60 = 0

• x^2 - 5x - 60 = 0

• x^2 + 5x - 60 = 0

The area of a triangular park 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 park using a quadratic equation.

• Height: 5 meters, Base: 9 meters

• Height: 8 meters, Base: 12 meters

• Height: 6 meters, Base: 10 meters

• Height: 10 meters, Base: 14 meters

A farmer wants to create a rectangular field with a perimeter of 100 meters. If the length is 10 meters more than the width, write a quadratic equation to find the dimensions of the field.

• Width = 15 meters, Length = 25 meters

• Width = 30 meters, Length = 40 meters

• Width = 20 meters, Length = 30 meters

• Width = 25 meters, Length = 35 meters

A rectangular piece of land has an area of 120 square meters. If the length is twice the width, identify the quadratic equation that represents this situation and solve for the dimensions.

• Width = 5 meters, Length = 10 meters

• Width = 7.75 meters, Length = 15.5 meters

• Width = 6 meters, Length = 12 meters

• Width = 8 meters, Length = 16 meters

A square garden has an area of 64 square meters. If the area is increased by 36 square meters, what will be the new side length? Write and solve the quadratic equation to find the answer.

• 14 meters

• 8 meters

• 10 meters

• 12 meters

A rectangular classroom has a length that is 2 meters less than twice its width. If the area of the classroom is 48 square meters, identify and solve the quadratic equation to find the dimensions of the classroom.

• Width: 4 meters, Length: 10 meters

• Width: 6 meters, Length: 6 meters

• Width: 5 meters, Length: 8 meters

• Width: 3 meters, Length: 9 meters

The area of a rectangular plot is 150 square meters. If the length is 5 meters more than the width, write the quadratic equation and find the dimensions of the plot.

• Width: 8 meters, Length: 18 meters

• Width: 12 meters, Length: 17 meters

• Width: 5 meters, Length: 20 meters

• Width: 10 meters, Length: 15 meters

A rectangular box has a length that is 4 inches longer than its width. If the area of the base of the box is 60 square inches, identify the quadratic equation and solve for the width.

• 6

• 8

• 4

• 10

A rectangular swimming pool has a length that is 3 meters longer than its width. If the area of the pool is 54 square meters, write the quadratic equation and find the dimensions of the pool.

• Width: 7 meters, Length: 10 meters

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

• Width: 4 meters, Length: 7 meters