Right Triangle Challenges: Pythagorean Problems for 8th Graders

A ladder is leaning against a wall. The foot of the ladder is 6 feet away from the wall, and the top reaches a height of 8 feet. Is the triangle formed by the ladder, the wall, and the ground a right triangle?

• No, it is an obtuse triangle.

• Yes, it is an isosceles triangle.

• No, it is a scalene triangle.

• Yes, it is a right triangle.

A triangular park has sides measuring 5 meters, 12 meters, and 13 meters. Determine if this park is a right triangle using the Pythagorean converse.

• Yes, but it has equal sides.

• Yes, the park is a right triangle.

• No, the park is a scalene triangle.

• No, the park is an obtuse triangle.

A rectangular garden has a diagonal that measures 10 meters. If one side is 6 meters, what is the length of the other side? Is the triangle formed by the sides and the diagonal a right triangle?

• 9 meters, no, it is not a right triangle.

• 10 meters, yes, it is a right triangle.

• 8 meters, yes, it is a right triangle.

• 7 meters, yes, it is a right triangle.

A right triangle has one leg measuring 9 cm and the other leg measuring 12 cm. What is the length of the hypotenuse? Verify if the triangle is a right triangle using the Pythagorean theorem.

• 14 cm

• 15 cm

• 13 cm

• 10 cm

A baseball diamond is a square with each side measuring 90 feet. What is the distance from home plate to second base? Is this distance a hypotenuse of a right triangle?

• 180 feet

• 45√2 feet

• 90√2 feet

• 90 feet

A ramp is built to help wheelchair access. If the ramp is 4 feet long and rises 3 feet, is the ramp forming a right triangle with the ground?

• No, the ramp is forming a square with the ground.

• Yes, the ramp is forming an obtuse triangle.

• No, the ramp is not forming any triangle.

• Yes, the ramp is forming a right triangle with the ground.

A triangle has sides measuring 7 cm, 24 cm, and 25 cm. Use the Pythagorean converse to determine if it is a right triangle.

• It is an obtuse triangle.

• Yes, it is a right triangle.

• It is an equilateral triangle.

• No, it is not a right triangle.

A 15-foot ladder is placed against a wall. If the base of the ladder is 9 feet from the wall, how high does the ladder reach? Is this a right triangle?

• 14 feet

• 10 feet

• 8 feet

• 12 feet

A triangular piece of land has sides of lengths 8 m, 15 m, and 17 m. Determine if this land is a right triangle using the Pythagorean theorem.

• Yes, it is a right triangle.

• No, it is an obtuse triangle.

• No, it is a scalene triangle.

• Yes, it is an isosceles triangle.

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

• The length of the other leg is 6 inches. No, this triangle is not a right triangle.

• The length of the other leg is 12 inches. Yes, this triangle is a right triangle.

• The length of the other leg is 10 inches. No, this triangle is not a right triangle.

• The length of the other leg is 8 inches. Yes, this triangle is a right triangle.