Quadratic Word Problems: Solve & Interpret for Grade 9

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: 8 meters, Length: 11 meters

• Width: 5 meters, Length: 8 meters

• Width: 7 meters, Length: 10 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) = -5t^2 + 10t + 1.5. How long will it take for the ball to hit the ground?

• 2 seconds

• 4 seconds

• 3 seconds

• 5 seconds

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

• 8 and 9

• 9 and 10

• 6 and 7

• 7 and 8

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

• 10

• 20

• 15

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?

• 2 seconds

• 4 seconds

• 3 seconds

• 1 second

The area of a triangle is given by the formula 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: 10 meters, Height: 6 meters

• Base: 16 meters, Height: 12 meters

• Base: 12 meters, Height: 8 meters

• Base: 14 meters, Height: 10 meters

A rectangular swimming pool is 2 meters longer than it is wide. If the perimeter of the pool is 32 meters, what are the dimensions of the pool?

• Width: 7 meters, Length: 9 meters

• Width: 5 meters, Length: 7 meters

• Width: 6 meters, Length: 8 meters

• Width: 8 meters, Length: 10 meters

A farmer wants to create a rectangular field with a fixed area of 200 square meters. If the length of the field is 5 meters more than its width, what are the dimensions of the field?

• Width: 5 meters, Length: 40 meters

• Width: 8 meters, Length: 13 meters

• Width: 10 meters, Length: 15 meters

• Width: 12 meters, Length: 18 meters

The height of a certain object is modeled by the equation h(t) = -4.9t^2 + 20t + 5, where t is the time in seconds. How long will it take for the object to reach the ground?

• 3.25 seconds

• 4.56 seconds

• 5.10 seconds

• 6.75 seconds

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

• Width: 5 cm, Length: 10 cm, Height: 2 cm

• Width: 4 cm, Length: 8 cm, Height: 1 cm

• Width: 6 cm, Length: 12 cm, Height: 3 cm

• Width: 7 cm, Length: 14 cm, Height: 4 cm

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