Factoring Fun: Real-Life Applications and Prime Factors

A gardener has a rectangular garden with an area of 48 square meters. If the length of the garden is 12 meters, what is the width of the garden? Use factoring to solve the equation.

• 6 meters

• 4 meters

• 8 meters

• 10 meters

A school is organizing a field trip for 120 students. They want to arrange them in equal groups. What are the possible group sizes? Use prime factorization to find the factors of 120.

• 7

• 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

• 11

• 9

A rectangular pool has a length that is 3 meters longer than its width. If the area of the pool is 54 square meters, what are the dimensions of the pool? Solve the equation by factoring.

• Width: 4 meters, Length: 7 meters

• Width: 5 meters, Length: 8 meters

• Width: 7 meters, Length: 10 meters

• Width: 6 meters, Length: 9 meters

A farmer has 36 apples and wants to pack them into boxes. If each box can hold the same number of apples, what are the possible numbers of apples per box? Use prime factorization to find the factors of 36.

• 10

• 7

• 1, 2, 3, 4, 6, 9, 12, 18, 36

• 5

A rectangular piece of land has a perimeter of 60 meters. If the length is 5 meters more than the width, what are the dimensions of the land? Solve the equation by factoring.

• Width: 10 meters, Length: 15 meters

• Width: 20 meters, Length: 25 meters

• Width: 5 meters, Length: 10 meters

• Width: 12.5 meters, Length: 17.5 meters

A pizza shop sells pizzas in sizes of 8, 12, and 16 inches. If they want to make a large pizza that is 48 inches in diameter, how many pizzas of each size can they make? Use prime factorization to find the combinations.

• 36 (8-inch), 16 (12-inch), 9 (16-inch)

• 40 (8-inch), 20 (12-inch), 10 (16-inch)

• 30 (8-inch), 10 (12-inch), 5 (16-inch)

• 24 (8-inch), 8 (12-inch), 4 (16-inch)

A rectangular garden has an area of 72 square feet. If the length is twice the width, what are the dimensions of the garden? Solve the equation by factoring.

• Width: 4 feet, Length: 8 feet

• Width: 3 feet, Length: 6 feet

• Width: 5 feet, Length: 10 feet

• Width: 6 feet, Length: 12 feet

A box has a volume of 120 cubic centimeters. If the height is 5 cm and the base is a square, what is the length of one side of the base? Use factoring to solve the equation.

• 3 cm

• 4√3 cm

• 6 cm

• 2√6 cm

A concert hall has 180 seats that need to be arranged in rows. If each row has the same number of seats, what are the possible numbers of seats per row? Use prime factorization to find the factors of 180.

• 7

• 8

• 11

• 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

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

• Width: 5 meters, Length: 9 meters

• Width: 7 meters, Length: 11 meters

• Width: 8 meters, Length: 12 meters

• Width: 6 meters, Length: 10 meters