Solving Real-World Quadratics: Find Unknown Dimensions

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: 5 meters, Length: 8 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?

• 3.10 seconds

• 1.75 seconds

• 2.24 seconds

• 4.50 seconds

A car's value decreases over time according to the equation V(t) = -2000t^2 + 20000, where V is the value in dollars and t is the time in years. After how many years will the car be worth $0?

• 5.75

• 4.00

• 3.16

• 2.50

The path of a projectile is modeled by the equation h(t) = -16t^2 + 32t + 48, where h is the height in feet and t is the time in seconds. What is the maximum height reached by the projectile?

• 48 feet

• 80 feet

• 64 feet

• 32 feet

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

• Width: 8 feet, Length: 16 feet

• Width: 12 feet, Length: 24 feet

• Width: 15 feet, Length: 30 feet

• Width: 10 feet, Length: 20 feet

A company finds that the profit P (in dollars) from selling x items is given by the equation P(x) = -5x^2 + 150x - 200. How many items should the company sell to maximize its profit?

• 25

• 10

• 20

• 15

The height of a triangle is 4 meters less than its base. If the area of the triangle is 48 square meters, what are the dimensions of the triangle?

• Base: 10 meters, Height: 6 meters

• Base: 12 meters, Height: 8 meters

• Base: 16 meters, Height: 12 meters

• Base: 14 meters, Height: 10 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: 20 meters, Length: 30 meters

• Width: 25 meters, Length: 30 meters

• Width: 15 meters, Length: 20 meters

• Width: 22.5 meters, Length: 27.5 meters

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

• 3 seconds

• 10 seconds

• 7 seconds

A rectangular box has a volume of 120 cubic centimeters. If the length is 2 centimeters more than the width and the height is 3 centimeters, what are the dimensions of the box?

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

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

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

• Width: 5 cm, Length: 5 cm, Height: 4 cm