Mastering Quadratic Equations: Real-World Challenges

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: 8 meters, Length: 11 meters

• Width: 7 meters, Length: 10 meters

• Width: 6 meters, Length: 9 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?

• 4.2 seconds

• 2.08 seconds

• 3.5 seconds

• 1.5 seconds

The path of a projectile can be modeled by the equation h(t) = -4.9t^2 + 10t + 1.5, where h is the height in meters and t is the time in seconds. When will the projectile reach its maximum height?

• 1.50 seconds

• 0.75 seconds

• 2.00 seconds

• 1.02 seconds

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?

• 5

• 20

• 10

• 15

A car's distance from a starting point can be modeled by the equation d(t) = 5t^2 + 20t, where d is the distance in meters and t is the time in seconds. How far will the car be after 4 seconds?

• 80 meters

• 120 meters

• 160 meters

• 200 meters

The area of a triangle is given by the formula A = 1/2 * base * height. If the base is 2 meters longer than the height and the area is 30 square meters, what are the dimensions of the triangle?

• Height: 4 meters, Base: 6 meters

• Height: 5 meters, Base: 7 meters

• Height: 10 meters, Base: 12 meters

• Height: 6 meters, Base: 8 meters

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

• Width: 10 meters, Length: 20 meters

• Width: 15 meters, Length: 30 meters

• Width: 12 meters, Length: 24 meters

• Width: 8 meters, Length: 16 meters

A farmer wants to create a rectangular field with a perimeter of 100 meters. If the length is 5 meters more than the width, what are the dimensions of the field?

• Width: 25 meters, Length: 30 meters

• Width: 22.5 meters, Length: 27.5 meters

• Width: 20 meters, Length: 30 meters

• Width: 15 meters, Length: 20 meters

The height of a ball thrown into the air can be modeled by the equation h(t) = -16t^2 + 32t + 48. At what time will the ball reach the ground?

• 3.0

• 5.5

• 4.0

• 2.5

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

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

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