Pythagorean Triples & Theorem: 8th Grade Challenge!

A ladder is leaning against a wall. The foot of the ladder is 6 feet from the wall, and the ladder reaches a height of 8 feet. Is the length of the ladder a Pythagorean triple?

• The length of the ladder is 10 feet, which is not a Pythagorean triple.

• Yes, the length of the ladder is a Pythagorean triple.

• Yes, but the ladder is too short to be a Pythagorean triple.

• No, the length of the ladder is not a Pythagorean triple.

A right triangle has one leg measuring 9 cm and the other leg measuring 12 cm. What is the length of the hypotenuse?

• 13 cm

• 17 cm

• 15 cm

• 10 cm

A rectangular garden has a length of 15 meters and a width of 20 meters. If you want to plant a diagonal path from one corner to the opposite corner, how long will the path be?

• 20 meters

• 25 meters

• 30 meters

• 15 meters

A 5-foot tall person is standing 12 feet away from a tree. If they look up at the top of the tree, what is the height of the tree if the angle of elevation is 60 degrees?

• 25 feet

• 30 feet

• 15 feet

• 20.78 feet

A right triangle has sides of lengths 7, 24, and 25. Verify if these lengths form a Pythagorean triple.

• Only two of the lengths form a Pythagorean triple.

• Yes, the lengths 7, 24, and 25 form a Pythagorean triple.

• The lengths 7, 24, and 25 can form a triangle, but not a right triangle.

• No, the lengths 7, 24, and 25 do not form a Pythagorean triple.

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

• 90 feet

• 180 feet

• 45√2 feet

• 90√2 feet

A right triangle has one leg measuring 8 inches and a hypotenuse measuring 10 inches. What is the length of the other leg?

• 8 inches

• 4 inches

• 6 inches

• 10 inches

A ramp is built to help wheelchair access to a building. If the ramp is 10 feet long and rises 6 feet, how far is the base of the ramp from the building?

• 8 feet

• 10 feet

• 12 feet

• 5 feet

A right triangle has legs of lengths 5 and 12. What is the area of this triangle?

• 30

• 36

• 24

• 60

A 30-foot tall flagpole casts a shadow that is 40 feet long. Using the Pythagorean theorem, find the distance from the top of the flagpole to the end of the shadow.

• 50 feet

• 40 feet

• 60 feet

• 30 feet