Quadratic Equations: Area and Dimensions Challenge

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: 8 meters, Length: 16 meters

• Width: 12 meters, Length: 24 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 reach the ground?

• 8 seconds

• 6 seconds

• 4 seconds

• 2 seconds

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

• 15 meters

• 20 meters

• 10 meters

• 12 meters

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

• 15 meters

• 20 meters

• 5 meters

• 10 meters

A swimming pool is in the shape of a square. If the area of the pool is 81 square meters, what is the length of one side of the pool?

• 9 meters

• 15 meters

• 6 meters

• 12 meters

A car's depreciation can be modeled by the equation v(t) = -4t^2 + 40t + 200, where v is the value of the car in dollars and t is the time in years. When will the car's value reach $0?

• 10 years

• 20 years

• 5 years

• Approximately 14.32 years

The area of a square plot of land is 64 square meters. What is the length of each side of the plot?

• 10 meters

• 8 meters

• 12 meters

• 6 meters

A ball is dropped from a height of 80 feet. The height of the ball after t seconds is given by the equation h(t) = -16t^2 + 80. How long will it take for the ball to hit the ground?

• 1.5 seconds

• 2.24 seconds

• 3.0 seconds

• 4.5 seconds

A rectangular swimming 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?

• Width: 7 meters, Length: 10 meters

• Width: 4 meters, Length: 7 meters

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

The area of a square garden is 36 square meters. What is the length of one side of the garden?

• 10 meters

• 8 meters

• 6 meters

• 4 meters