Real-Life Quadratics: Factoring & Solving Challenges

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

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

• Width: 4 meters, Length: 7 meters

• Width: 3 meters, Length: 6 meters

The product of two consecutive integers is 72. What are the integers?

• 9 and 10

• 6 and 7

• 7 and 8

• 8 and 9

A ball is thrown upwards from a height of 5 meters with an initial velocity of 10 meters per second. The height of the ball in meters after t seconds is given by the equation h(t) = -5t^2 + 10t + 5. When will the ball hit the ground?

• 3.0 seconds

• Approximately 2.414 seconds

• 4.2 seconds

• 1.5 seconds

The area of a triangular field is 60 square meters. If the base is 4 meters longer than the height, find the dimensions of the field.

• Height: 8 meters, Base: 12 meters

• Height: 10 meters, Base: 14 meters

• Height: 5 meters, Base: 9 meters

• Height: 15 meters, Base: 19 meters

A rectangular pool has a length that is twice its width. If the area of the pool is 288 square feet, what are the dimensions of the pool?

• Width: 10 feet, Length: 20 feet

• Width: 15 feet, Length: 30 feet

• Width: 12 feet, Length: 24 feet

• Width: 8 feet, Length: 16 feet

A car's value decreases according to the equation V(t) = -200t^2 + 4000, where V is the value in dollars and t is the time in years. When will the car's value reach zero?

• 2.5 years

• 5.0 years

• 4.47 years

• 3.2 years

The difference between the squares of two numbers is 45. If one number is 5 more than the other, find the two numbers.

• 6 and 1

• 7 and 2

• 10 and 5

• 8 and 3

A rectangular piece of land has a length that is 6 meters longer than its width. If the area of the land is 72 square meters, what are the dimensions of the land?

• Width: 4 meters, Length: 10 meters

• Width: 5 meters, Length: 11 meters

• Width: 6 meters, Length: 12 meters

• Width: 8 meters, Length: 14 meters

The height of a projectile is modeled by the equation h(t) = -16t^2 + 32t + 48. When will the projectile reach its maximum height?

• 1 second

• 0.5 seconds

• 2 seconds

• 3 seconds

A rectangular box has a volume of 120 cubic centimeters. If the length is 2 centimeters longer than the width and the height is 3 centimeters, find the dimensions of the box.

• Width: 5 cm, Length: 7 cm, Height: 3 cm

• Width: 6 cm, Length: 8 cm, Height: 3 cm

• Width: 4 cm, Length: 6 cm, Height: 3 cm

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