Factoring Quadratics in Real-Life Word Problems

A rectangular garden has an area of 48 square meters. If the length of the garden is 4 meters more than its width, what are the dimensions of the garden?

• Width: 4 meters, Length: 8 meters

• Width: 3 meters, Length: 7 meters

• Width: 5 meters, Length: 9 meters

• Width: 6 meters, Length: 10 meters

A company produces a certain type of gadget, and the profit, P, in dollars, can be modeled by the equation P = x^2 + 6x - 16, where x is the number of gadgets sold. How many gadgets must be sold to break even?

• -2

• 4

• 0

• 2

The area of a triangular park is represented by the expression 3x^2 + 12x. If the base of the triangle is 3x, what is the height of the park in terms of x?

• 2x + 8

• 4x + 6

• 3x + 10

• x + 12

A rectangular pool has a length that is 5 meters longer than its width. If the area of the pool is 60 square meters, what are the dimensions of the pool?

• Width: 6 meters, Length: 11 meters

• Width: 4 meters, Length: 9 meters

• Width: 7 meters, Length: 12 meters

• Width: 5 meters, Length: 10 meters

A farmer has a rectangular field with an area of 72 square meters. If the length is 2 meters less than twice the width, what are the dimensions of the field?

• Length: 14 meters, Width: 4 meters

• Length: 12 meters, Width: 6 meters

• Length: 8 meters, Width: 9 meters

• Length: 10 meters, Width: 6 meters

The area of a rectangular plot is given by the expression x^2 - 9. If the width of the plot is x - 3, what is the length of the plot?

• x - 3

• x^2 + 3

• x + 9

• x + 3

A box is to be constructed with a square base and an open top. If the volume of the box is represented by the expression x^3 - 64, what is the area of the base in terms of x?

• (x^3 - 64)^(2/3)

• (x^3 - 64)^(1/3)

• x^3 + 64

• x^2 - 64

A rectangular piece of land has a length that is 3 meters longer than its width. If the area of the land is 40 square meters, what are the dimensions of the land?

• Width: 3 meters, Length: 6 meters

• Width: 6 meters, Length: 9 meters

• Width: 4 meters, Length: 7 meters

• Width: 5 meters, Length: 8 meters

The area of a rectangular garden is represented by the expression 2x^2 + 8x. If the length of the garden is 2x, what is the width of the garden?

• x + 4

• 2x + 2

• 2x + 4

• x + 2

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: 6 feet, Length: 10 feet

• Width: 8 feet, Length: 12 feet

• Width: 5 feet, Length: 9 feet

• Width: 7 feet, Length: 11 feet