Quadratic Equations: Solve Real-World Problems

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 70 square meters, what are the dimensions of the garden?

• Width: 6 meters, Length: 9 meters

• Width: 7 meters, Length: 10 meters

• Width: 8 meters, Length: 11 meters

• Width: 5 meters, Length: 8 meters

A ball is thrown upwards from a height of 1.5 meters with an initial velocity of 10 meters per second. How long will it take for the ball to hit the ground?

• 3.00 seconds

• 4.50 seconds

• 2.12 seconds

• 1.75 seconds

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

• 8 and 9

• 7 and 8

• 9 and 10

• 6 and 7

A car's value decreases according to the equation V(t) = -2t^2 + 20t + 100, where V is the value in thousands of dollars and t is the number of years since purchase. When will the car's value reach $0?

• Approximately 5.5 years

• Approximately 12.32 years

• Approximately 8.75 years

• Approximately 15 years

A projectile is launched from the ground with an initial velocity of 50 meters per second. The height of the projectile after t seconds is given by the equation h(t) = -5t^2 + 50t. How long will it take for the projectile to reach its maximum height?

• 5 seconds

• 10 seconds

• 7 seconds

• 3 seconds

The area of a triangle is given by the equation A = 1/2 * base * height. If the base is 4 meters longer than the height and the area is 48 square meters, what are the base and height of the triangle?

• Base: 14 meters, Height: 10 meters

• Base: 12 meters, Height: 8 meters

• Base: 10 meters, Height: 6 meters

• Base: 8 meters, Height: 4 meters

A rectangular swimming pool has a length that is twice its width. If the area of the pool is 200 square meters, what are the dimensions of the pool?

• Width: 8 meters, Length: 16 meters

• Width: 15 meters, Length: 30 meters

• Width: 10 meters, Length: 20 meters

• Width: 5 meters, Length: 10 meters

A farmer wants to create a rectangular pen for his sheep. He has 60 meters of fencing. If the length of the pen is 5 meters more than its width, what are the dimensions of the pen?

• Width: 15 meters, Length: 20 meters

• Width: 10 meters, Length: 15 meters

• Width: 20 meters, Length: 25 meters

• Width: 12.5 meters, Length: 17.5 meters

The height of a ball thrown into the air can be modeled by the equation h(t) = -4.9t^2 + 20t + 1, where h is the height in meters and t is the time in seconds. When will the ball hit the ground?

• 6.0 seconds

• 4.08 seconds

• 5.2 seconds

• 3.5 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, what are the dimensions of the box?

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

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

• Width: 10 cm, Length: 12 cm, Height: 3 cm

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