Quadratics and Pythagorean Theorem: Solving Word Problems

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 40 square meters, what are the dimensions of the garden? Graph the quadratic function representing the area.

• Width: 4 meters, Length: 7 meters

• Width: 6 meters, Length: 9 meters

• Width: 5 meters, Length: 10 meters

• Width: 5 meters, Length: 8 meters

A right triangle has one leg that is 2 meters longer than the other leg. If the hypotenuse is 10 meters, find the lengths of the legs. Use a quadratic equation to solve and graph the relationship.

• 3 meters and 5 meters

• 5 meters and 7 meters

• 4 meters and 6 meters

• The lengths of the legs are 6 meters and 8 meters.

The height of a projectile is modeled by the equation h(t) = -4.9t^2 + 20t + 5, where h is the height in meters and t is the time in seconds. At what time does the projectile hit the ground? Graph the quadratic function to visualize the height over time.

• 4.24 seconds

• 6.1 seconds

• 5.0 seconds

• 3.5 seconds

A ladder is leaning against a wall. The foot of the ladder is 4 feet from the wall, and the ladder is 10 feet long. How high up the wall does the ladder reach? Use the Pythagorean theorem to set up a quadratic equation and solve for the height.

• 6 feet

• 8 feet

• 5 feet

• 2 * sqrt(21) feet

A ball is thrown upwards from a height of 1.5 meters with an initial velocity of 15 m/s. The height of the ball can be modeled by the equation h(t) = -4.9t^2 + 15t + 1.5. When will the ball reach its maximum height? Graph the function to find the vertex.

• 1.53 seconds

• 1.25 seconds

• 2.00 seconds

• 0.75 seconds

The area of a triangular park is 60 square meters. If the base is 5 meters longer than the height, find the dimensions of the park. Set up a quadratic equation and graph the function to show the relationship between base and height.

• Height: 10 meters, Base: 15 meters

• Height: 8 meters, Base: 13 meters

• Height: 12 meters, Base: 17 meters

• Height: 5 meters, Base: 10 meters

A rectangular swimming pool has a width that is half its length. If the perimeter of the pool is 60 meters, find the dimensions of the pool. Use a quadratic equation to express the relationship and graph it.

• Length: 10 meters, Width: 20 meters

• Length: 25 meters, Width: 5 meters

• Length: 20 meters, Width: 10 meters

• Length: 15 meters, Width: 30 meters

A right triangle has a hypotenuse of 13 cm and one leg that is 5 cm longer than the other leg. Find the lengths of the legs using the Pythagorean theorem and graph the quadratic equation that represents the relationship.

• 7 cm and 10 cm

• 5 cm and 12 cm

• The lengths of the legs are 8 cm and 13 cm.

• 6 cm and 9 cm

A car's distance from a starting point is modeled by the equation d(t) = 3t^2 + 12t, where d is in meters and t is in seconds. How far is the car from the starting point after 4 seconds? Graph the quadratic function to visualize the distance over time.

• 96 meters

• 84 meters

• 72 meters

• 120 meters

A rectangular field has a length that is twice its width. If the area of the field is 200 square meters, find the dimensions of the field. Set up a quadratic equation and graph the function to illustrate the relationship between length and width.

• Length: 25 meters, Width: 5 meters

• Length: 30 meters, Width: 15 meters

• Length: 40 meters, Width: 20 meters

• Length: 20 meters, Width: 10 meters