Quadratics in Action: Area Challenges 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?

• Width: 7 meters, Length: 10 meters

• Width: 5 meters, Length: 8 meters

• Width: 8 meters, Length: 11 meters

• Width: 6 meters, Length: 9 meters

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

• 10

• 5

• 3

• 7

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.

• Height: 10 meters, Base: 14 meters

• Height: 8 meters, Base: 12 meters

• Height: 5 meters, Base: 9 meters

• Height: 6 meters, Base: 10 meters

A rectangular field has a length that is twice its width. If the area of the field is 200 square meters, what are the dimensions of the field?

• Width: 10 meters, Length: 20 meters

• Width: 12 meters, Length: 24 meters

• Width: 5 meters, Length: 15 meters

• Width: 8 meters, Length: 16 meters

A square plot of land has an area of (x^2) square meters. If the side length of the plot is increased by 2 meters, what will be the new area in terms of x?

• x^2 + 4x + 2

• x^2 + 2x

• x^2 + 4x + 4

• x^2 + 8

A rectangular box has a length of (2x + 1) meters, a width of (x - 1) meters, and a height of 3 meters. If the volume of the box is 60 cubic meters, find the value of x.

• 4.5

• 5

• 3.5

• 2

The area of a trapezoidal garden is given by the formula A = 1/2 * (b1 + b2) * h. If the bases are 5 meters and 7 meters, and the area is 60 square meters, find the height of the garden.

• 8 meters

• 12 meters

• 15 meters

• 10 meters

A rectangular room has a length that is 4 meters longer than its width. If the area of the room is 96 square meters, what are the dimensions of the room?

• Width: 5 meters, Length: 9 meters

• Width: 6 meters, Length: 10 meters

• Width: 10 meters, Length: 14 meters

• Width: 8 meters, Length: 12 meters

A rectangular piece of land has a length of (x + 3) meters and a width of (x - 2) meters. If the area of the land is 50 square meters, find the value of x.

• 5

• 10

• 3

• 7

A circular garden has a radius of (x + 1) meters. If the area of the garden is 50π square meters, find the value of x.

• 4

• 3

• 6√2 - 1

• 5√2 - 1