Solving Quadratic Equations in 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: 7 meters, Length: 10 meters

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

• Width: 8 meters, Length: 11 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

• 4.50 seconds

• 2.24 seconds

The area of a triangular park is 120 square meters. If the base of the triangle is 5 meters longer than its height, find the dimensions of the park. Use the formula for the area of a triangle: Area = 1/2 * base * height.

• Height: 12 meters, Base: 17 meters

• Height: 10 meters, Base: 15 meters

• Height: 18 meters, Base: 23 meters

• Height: 15 meters, Base: 20 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: 10 meters, Length: 20 meters

• Width: 8 meters, Length: 16 meters

• Width: 15 meters, Length: 30 meters

• Width: 5 meters, Length: 10 meters

A farmer wants to create a rectangular field with an area of 1500 square meters. If the length of the field is 10 meters more than its width, what are the dimensions of the field?

• Width: 20 meters, Length: 30 meters

• Width: 25 meters, Length: 35 meters

• Width: 35 meters, Length: 45 meters

• Width: 30 meters, Length: 40 meters

The area of a square is represented by the equation A = x^2. If the area of the square is 64 square meters, what is the length of one side of the square?

• 12 meters

• 10 meters

• 8 meters

• 6 meters

A rectangular plot of land has a length that is 4 meters less than twice its width. If the area of the plot is 96 square meters, find the dimensions of the plot.

• Length: 10 meters, Width: 9 meters

• Length: 14 meters, Width: 7 meters

• Length: 12 meters, Width: 8 meters

• Length: 16 meters, Width: 6 meters

A company produces a certain product, and the profit in dollars can be modeled by the equation P(x) = -2x^2 + 12x - 16, where x is the number of units sold. How many units must be sold to maximize profit?

• 5

• 4

• 2

• 3

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, find the dimensions of the box.

• Width: 10 cm, Length: 12 cm, Height: 1 cm

• Width: 5 cm, Length: 7 cm, Height: 4 cm

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

• Width: 4 cm, Length: 6 cm, Height: 5 cm

A rectangular garden has a perimeter of 60 meters. If the length is 5 meters more than the width, what are the dimensions of the garden?

• Width: 12.5 meters, Length: 17.5 meters

• Width: 10 meters, Length: 15 meters

• Width: 15 meters, Length: 20 meters

• Width: 20 meters, Length: 25 meters