Right Triangle Exploration: Pythagorean Challenges for 8th Graders

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 on the wall. Is the ladder forming a right triangle?

• No, the ladder is not forming a right triangle.

• The ladder is forming an acute triangle.

• The ladder is forming an obtuse triangle.

• Yes, the ladder is forming a right triangle.

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

• 13 cm

• 15 cm

• 10 cm

• 14 cm

A park has a triangular section where one side is 9 meters, another side is 12 meters, and the angle between them is a right angle. Calculate the length of the third side.

• 14 meters

• 10 meters

• 13 meters

• 15 meters

You are building a rectangular garden that is 10 feet long and 24 feet wide. What is the length of the diagonal that separates the two opposite corners?

• 30 feet

• 22 feet

• 20 feet

• 26 feet

A right triangle has sides of lengths 7 and 24. What is the length of the hypotenuse? Is this a Pythagorean triple?

• The length of the hypotenuse is 24, and it is not a Pythagorean triple.

• The length of the hypotenuse is 26, and it is not a Pythagorean triple.

• The length of the hypotenuse is 23, and it is a Pythagorean triple.

• The length of the hypotenuse is 25, and it is a Pythagorean triple.

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

• 8 cm

• 14 cm

• 10 cm

• 12 cm

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

• 45√2 feet

• 90√2 feet

• 180 feet

• 90 feet

A right triangle has legs measuring 8 inches and 15 inches. What is the length of the hypotenuse?

• 12 inches

• 10 inches

• 17 inches

• 20 inches

A 30-foot tall tree casts a shadow that is 40 feet long. Is the tree, the ground, and the shadow forming a right triangle?

• No, the shadow is too long for a triangle.

• Yes, but only if the tree is leaning.

• Yes, the tree, the ground, and the shadow are forming a right triangle.

• No, the tree and shadow do not form a triangle.

A right triangle has sides of lengths 9, 12, and 15. Verify if these lengths form a Pythagorean triple.

• No, these lengths do not form a Pythagorean triple.

• These lengths form an acute triangle.

• The lengths are not integers.

• Yes, these lengths form a Pythagorean triple.