9th Grade Quadratics & Pythagorean Theorem Challenges

A ladder is leaning against a wall. The foot of the ladder is 3 feet away from the wall, and the ladder is 12 feet long. How high up the wall does the ladder reach? Use the Pythagorean theorem to find the height.

• 9.5 feet

• 10 feet

• 13 feet

• 11.62 feet

A rectangular garden has a length that is 4 meters longer than its width. If the area of the garden is 60 square meters, find the dimensions of the garden using a quadratic equation.

• Width: 7 meters, Length: 11 meters

• Width: 8 meters, Length: 12 meters

• Width: 6 meters, Length: 10 meters

• Width: 5 meters, Length: 9 meters

A right triangle has one leg that is 5 cm longer than the other leg. If the hypotenuse is 13 cm, find the lengths of both legs using the Pythagorean theorem.

• Shorter leg: 5 cm, Longer leg: 10 cm

• Shorter leg: 6 cm, Longer leg: 11 cm

• Shorter leg: 7 cm, Longer leg: 12 cm

• Shorter leg: 8 cm, Longer leg: 13 cm

The height of a triangular park is 6 meters less than twice its base. If the area of the park is 48 square meters, find the base and height using a quadratic equation.

• Base: 9 meters, Height: 12 meters

• Base: 12 meters, Height: 18 meters

• Base: 6 meters, Height: 6 meters

• Base: 8 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, find the dimensions of the pool using a quadratic equation.

• 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 right triangle has legs of lengths x and x + 4. If the hypotenuse is 10, find the lengths of the legs using the Pythagorean theorem.

• 6 and 10

• 8 and 12

• 5 and 9

• 7 and 11

A rectangular field has a length that is 3 meters more than twice its width. If the area of the field is 75 square meters, find the dimensions of the field using a quadratic equation.

• Width: 7 meters, Length: 17 meters

• Width: 5 meters, Length: 13 meters

• Width: 6 meters, Length: 15 meters

• Width: 4 meters, Length: 11 meters

A right triangle has one leg that is 7 cm and the hypotenuse is 25 cm. Find the length of the other leg using the Pythagorean theorem.

• 20 cm

• 15 cm

• 18 cm

• 24 cm

A rectangular box has a length that is 3 cm longer than its width. If the volume of the box is 60 cubic centimeters and the height is 5 cm, find the dimensions of the box using a quadratic equation.

• Width: 3 cm, Length: 6 cm, Height: 5 cm

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

• Width: 1 cm, Length: 4 cm, Height: 5 cm

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

A right triangle has one leg that is 8 cm and the other leg is 6 cm. Calculate the length of the hypotenuse using the Pythagorean theorem.

• 10 cm

• 12 cm

• 9 cm

• 7 cm