Exploring Quadratic Equations and Area Calculations

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: 6 meters, Length: 9 meters

• Width: 8 meters, Length: 11 meters

• Width: 5 meters, Length: 8 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 dimensions of the pool.

• Width: 5 meters, Length: 10 meters

• Width: 4 meters, Length: 11 meters

• Width: 6 meters, Length: 9 meters

• Width: 3 meters, Length: 15 meters

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, what are the dimensions of the park?

• Height: 6 meters, Base: 10 meters

• Height: 8 meters, Base: 12 meters

• Height: 5 meters, Base: 9 meters

• Height: 10 meters, Base: 14 meters

A square plot of land has an area of (x^2 + 16x + 64) square meters. What is the length of one side of the plot?

• x + 16

• x + 2

• x + 8

• x + 4

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: 5 meters, Length: 15 meters

• Width: 8 meters, Length: 16 meters

• Width: 12 meters, Length: 24 meters

A rectangular box has a length of (x + 2) meters, a width of (x - 1) meters, and a height of 5 meters. If the volume of the box is 100 cubic meters, find the value of x.

• 6.75

• 4.22

• 3.14

• 5.00

The area of a trapezoid is given by the formula A = 1/2 * (b1 + b2) * h. If the bases are (x + 3) and (x + 5) and the height is 4 meters, and the area is 32 square meters, find the value of x.

• 2

• 6

• 8

• 4

A rectangular garden has a length of (2x + 4) meters and a width of (x + 2) meters. If the area of the garden is 48 square meters, find the value of x.

• 8

• 6

• 4

• 2

A rectangular room has a length that is 4 meters longer than its width. If the area of the room is 60 square meters, what are the dimensions of the room?

• Width: 5 meters, Length: 9 meters

• Width: 7 meters, Length: 11 meters

• Width: 8 meters, Length: 12 meters

• Width: 6 meters, Length: 10 meters

A rectangular plot of land has a length of (x + 3) meters and a width of (x - 1) meters. If the area of the plot is 30 square meters, find the dimensions of the plot.

• Length: 6 meters, Width: 2 meters

• Length: 4 meters, Width: 7 meters

• Length: 8 meters, Width: 1 meter

• Length: 5 meters, Width: 3 meters