Quadratic Equations: Real-World Problem Solving

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: 5 meters, Length: 8 meters

• Width: 8 meters, Length: 11 meters

• Width: 7 meters, Length: 10 meters

• Width: 6 meters, Length: 9 meters

A ball is thrown upwards from a height of 1.5 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) = -4.9t^2 + 10t + 1.5. How long will it take for the ball to hit the ground?

• 1.75 seconds

• 3.10 seconds

• 2.24 seconds

• 4.50 seconds

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

• 9 and 10

• 8 and 9

• 7 and 8

• 6 and 7

A company finds that the profit P (in dollars) from selling x items is given by the equation P(x) = -2x^2 + 40x - 100. How many items should the company sell to maximize its profit?

• 10

• 5

• 15

• 20

A projectile is launched from the ground with an initial velocity of 20 meters per second. The height h (in meters) of the projectile after t seconds is given by h(t) = -5t^2 + 20t. When will the projectile reach its maximum height?

• 4 seconds

• 2 seconds

• 1 second

• 3 seconds

The area of a triangular field is 120 square meters. If the base of the triangle is 10 meters, what is the height of the triangle?

• 30 meters

• 12 meters

• 18 meters

• 24 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: 5 meters, Length: 10 meters

• Width: 15 meters, Length: 30 meters

• Width: 8 meters, Length: 16 meters

• Width: 10 meters, Length: 20 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: 20 meters, Length: 25 meters

• Width: 12.5 meters, Length: 17.5 meters

• Width: 10 meters, Length: 15 meters

The height of a certain plant is modeled by the equation h(t) = -3t^2 + 12t + 5, where h is the height in centimeters and t is the time in weeks. When will the plant reach its maximum height?

• 1 week

• 4 weeks

• 3 weeks

• 2 weeks

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

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

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

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