Solving Quadratic Word Problems: Contextual Challenges

A rectangular garden has an area of 144 square meters. If the length is twice the width, what are the dimensions of the garden?

• Width: 6√2 meters, Length: 12√2 meters

• Width: 10 meters, Length: 20 meters

• Width: 8 meters, Length: 16 meters

• Width: 4√2 meters, Length: 8√2 meters

The height of a ball thrown into the air can be modeled by the equation h(t) = -16t^2 + 64t, where h is the height in feet and t is the time in seconds. How long will it take for the ball to hit the ground?

• 4 seconds

• 8 seconds

• 6 seconds

• 2 seconds

A square park has an area of 225 square meters. What is the length of one side of the park?

• 12 meters

• 15 meters

• 20 meters

• 10 meters

The area of a triangle is given by the formula A = 1/2 * base * height. If the base is 10 meters and the area is 50 square meters, what is the height of the triangle?

• 20 meters

• 10 meters

• 15 meters

• 5 meters

A swimming pool is in the shape of a square. If the area of the pool is 256 square feet, what is the length of one side of the pool?

• 16 feet

• 14 feet

• 12 feet

• 20 feet

A car's depreciation can be modeled by the equation V(t) = V0 - kt^2, where V0 is the initial value, k is a constant, and t is time in years. If the car's value is $0 after 5 years, what was the initial value if k is 4?

• 200

• 100

• 75

• 50

The area of a circular flower bed is 78.5 square feet. What is the radius of the flower bed? (Use π ≈ 3.14)

• 5 feet

• 7 feet

• 10 feet

• 3 feet

A rectangular box has a volume of 512 cubic inches. If the height is 8 inches and the length is twice the width, what are the dimensions of the box?

• Width: 5 inches, Length: 10 inches, Height: 8 inches

• Width: 4√2 inches, Length: 8√2 inches, Height: 8 inches

• Width: 2 inches, Length: 4 inches, Height: 8 inches

• Width: 6 inches, Length: 12 inches, Height: 8 inches

The area of a square is 64 square meters. What is the length of one side of the square?

• 8 meters

• 12 meters

• 10 meters

• 6 meters

A ball is dropped from a height of 64 feet. The height of the ball after t seconds is given by the equation h(t) = -16t^2 + 64. How long will it take for the ball to reach the ground?

• 4 seconds

• 3 seconds

• 2 seconds

• 1 second