Solving Real-Life Quadratic Problems in Geometry

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: 6 meters, Length: 9 meters

• Width: 7 meters, Length: 10 meters

• Width: 8 meters, Length: 11 meters

• Width: 5 meters, Length: 8 meters

A rectangular swimming pool has a width that is half its length. If the area of the pool is 200 square meters, find the dimensions of the pool using the quadratic formula.

• Length: 15 meters, Width: 7.5 meters

• Length: 25 meters, Width: 12.5 meters

• Length: 30 meters, Width: 15 meters

• Length: 20 meters, Width: 10 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: 8 meters, Base: 12 meters

• Height: 5 meters, Base: 9 meters

• Height: 10 meters, Base: 14 meters

• Height: 6 meters, Base: 10 meters

A rectangular field has a length that is 5 meters less than twice its width. If the area of the field is 60 square meters, determine the dimensions of the field.

• Width: 7 meters, Length: 9 meters

• Width: 4 meters, Length: 12 meters

• Width: 8 meters, Length: 6 meters

• Width: 5 meters, Length: 10 meters

A square plot of land has an area of 144 square meters. If the owner wants to increase the area by 36 square meters, what will be the new side length of the square?

• 10 meters

• 12 meters

• 15 meters

• 13.42 meters

A rectangular box has a length that is 2 meters longer than its width. If the volume of the box is 120 cubic meters and the height is 5 meters, find the width of the box using the quadratic formula.

• 4

• 6

• 8

• 2

The area of a trapezoidal garden is 120 square meters. If the lengths of the two parallel sides are 10 meters and 14 meters, what is the height of the garden?

• 12 meters

• 8 meters

• 10 meters

• 15 meters

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

• Width: 8 feet, Length: 12 feet

• Width: 6 feet, Length: 10 feet

• Width: 5 feet, Length: 9 feet

• Width: 7 feet, Length: 11 feet

A farmer wants to create a rectangular pen for his sheep. If the length is 3 meters more than twice the width and the area is 75 square meters, find the dimensions of the pen.

• Width: 7 meters, Length: 17 meters

• Width: 5 meters, Length: 13 meters

• Width: 6 meters, Length: 15 meters

• Width: 4 meters, Length: 10 meters

A rectangular billboard has a width that is 2 meters less than its length. If the area of the billboard is 50 square meters, what are the dimensions of the billboard?

• Length: 8 meters, Width: 6 meters

• Length: 10 meters, Width: 8 meters

• Length: 12 meters, Width: 10 meters

• Length: 9 meters, Width: 7 meters