Pythagorean Triangle Challenges for Grade 8 Students

A ladder is leaning against a wall. The foot of the ladder is 6 feet away from the wall, and the ladder reaches a height of 8 feet on the wall. Is the ladder the correct length according to the Pythagorean theorem?

• The ladder is 12 feet long according to the Pythagorean theorem.

• Yes, the ladder is 10 feet long according to the Pythagorean theorem.

• The ladder is 8 feet long according to the Pythagorean theorem.

• The ladder is 14 feet long according to the Pythagorean theorem.

A right triangle has one leg measuring 5 cm and the other leg measuring 12 cm. What is the length of the hypotenuse?

• 10 cm

• 13 cm

• 14 cm

• 15 cm

A rectangular park has a length of 30 meters and a width of 40 meters. If you want to walk diagonally across the park, how far will you walk?

• 20 meters

• 50 meters

• 70 meters

• 60 meters

A right triangle has a hypotenuse of 13 inches and one leg measuring 5 inches. What is the length of the other leg?

• 6 inches

• 10 inches

• 12 inches

• 8 inches

A baseball diamond is a square with each side measuring 90 feet. What is the distance from home plate to second base?

• 180 feet

• 45√2 feet

• 90 feet

• 90√2 feet

A ramp is built to help wheelchair access. If the ramp rises 4 feet over a horizontal distance of 3 feet, what is the length of the ramp?

• 5 feet

• 3 feet

• 4 feet

• 6 feet

A right triangle has angles of 90 degrees, 45 degrees, and 45 degrees. If one leg measures 10 cm, what is the length of the hypotenuse?

• 14.14 cm

• 7.07 cm

• 10 cm

• 20 cm

A right triangle has a hypotenuse of 15 meters and one leg measuring 9 meters. Calculate the length of the other leg using the Pythagorean theorem.

• 14 meters

• 10 meters

• 8 meters

• 12 meters

A kite is flying at a height of 30 feet, and the string makes a 60-degree angle with the ground. If the string is 50 feet long, how far is the kite from the point directly below it on the ground?

• 20 feet

• 40 feet

• 25 feet

• 30 feet