Factoring for Real-Life Dimensions and Arrangements

A gardener has a rectangular flower bed with an area of 24 square meters. If the length of the bed is 2 meters more than its width, what are the dimensions of the flower bed?

• Width: 2 meters, Length: 4 meters

• Width: 4 meters, Length: 6 meters

• Width: 5 meters, Length: 7 meters

• Width: 3 meters, Length: 5 meters

A school is organizing a play and needs to arrange seats in rows. If the total number of seats is 60 and they want to arrange them in rows of equal length, what are the possible row arrangements using factoring?

• The possible row arrangements are: 1 row of 60 seats, 2 rows of 30 seats, 3 rows of 20 seats, 4 rows of 15 seats, 5 rows of 12 seats, 6 rows of 10 seats, 10 rows of 6 seats, 12 rows of 5 seats, 15 rows of 4 seats, 20 rows of 3 seats, 30 rows of 2 seats, and 60 rows of 1 seat.

• 9 rows of 6 seats

• 8 rows of 7 seats

• 7 rows of 8 seats

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

• Width: 5 meters, Length: 8 meters

• Width: 4 meters, Length: 7 meters

• Width: 6 meters, Length: 9 meters

• Width: 3 meters, Length: 6 meters

A farmer has a rectangular field with an area of 48 acres. If the length is 4 acres more than the width, what are the dimensions of the field?

• Width: 8 acres, Length: 12 acres

• Width: 6 acres, Length: 10 acres

• Width: 7 acres, Length: 11 acres

• Width: 5 acres, Length: 9 acres

A box has a volume of 120 cubic centimeters. If the length is twice the width and the height is 5 centimeters, what are the dimensions of the box?

• Width: 1 cm, Length: 2 cm, Height: 5 cm

• Width: 4 cm, Length: 8 cm, Height: 5 cm

• Width: 3 cm, Length: 6 cm, Height: 5 cm

• Width: 2√3 cm, Length: 4√3 cm, Height: 5 cm

A rectangle has a perimeter of 50 meters. If the length is 5 meters more than the width, what are the dimensions of the rectangle?

• Width: 10 meters, Length: 15 meters

• Width: 8 meters, Length: 13 meters

• Width: 12 meters, Length: 17 meters

• Width: 5 meters, Length: 10 meters

A company produces two types of widgets. The total production is represented by the polynomial x^2 + 5x + 6. If the production of the first type is represented by (x + 2)(x + 3), how many of the second type are produced?

• 3

• 2

• 1

• 0

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

• Width: 6 meters, Length: 10 meters

• Width: 7 meters, Length: 11 meters

• Width: 5 meters, Length: 9 meters

• Width: 8 meters, Length: 12 meters

A rectangular piece of land has an area of 72 square meters. If the length is 6 meters more than the width, what are the dimensions of the land?

• Width: 8 meters, Length: 14 meters

• Width: 4 meters, Length: 10 meters

• Width: 5 meters, Length: 11 meters

• Width: 6 meters, Length: 12 meters

A rectangular storage unit has a length that is 2 meters longer than its width. If the area of the storage unit is 30 square meters, what are the dimensions of the unit?

• Width: 3 meters, Length: 5 meters

• Width: 6 meters, Length: 8 meters

• Width: 4 meters, Length: 6 meters

• Width: 5 meters, Length: 7 meters