Exploring Pythagorean Triples and Right Triangles

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 this a Pythagorean triple? If so, what is the length of the ladder?

• 8 feet

• 14 feet

• 12 feet

• 10 feet

A right triangle has one leg measuring 5 cm and the other leg measuring 12 cm. Calculate the length of the hypotenuse and determine if the sides form a Pythagorean triple.

• The length of the hypotenuse is 15 cm and the sides form a Pythagorean triple.

• The length of the hypotenuse is 10 cm and the sides do not form a Pythagorean triple.

• The length of the hypotenuse is 13 cm and the sides form a Pythagorean triple.

• The length of the hypotenuse is 12 cm and the sides form a Pythagorean triple.

You are designing a triangular garden with one side measuring 9 meters and another side measuring 12 meters. What is the length of the third side if it forms a right triangle?

• 8 meters

• 7.94 meters

• 6 meters

• 10 meters

A right triangle is graphed on a coordinate plane with vertices at (0,0), (0,4), and (3,0). Calculate the length of the hypotenuse and confirm if the triangle is a right triangle using the Pythagorean theorem.

• 6

• 4

• 5

• 7

A baseball diamond is a square with each side measuring 90 feet. If a player runs from home plate to second base, how far does the player run? Use the Pythagorean theorem to find the distance.

• 180 feet

• 45√2 feet

• 90 feet

• 90√2 feet

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

• 50 meters

• 70 meters

• 30 meters

• 40 meters

A right triangle has legs measuring 7 inches and 24 inches. Find the length of the hypotenuse and check if the triangle is a Pythagorean triple.

• 30 inches

• 26 inches

• 25 inches

• 20 inches

You are building a ramp for a skateboard park. The ramp needs to rise 5 feet over a horizontal distance of 12 feet. What is the length of the ramp?

• 15 feet

• 12 feet

• 10 feet

• 13 feet

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

• 6 cm

• 4 cm

• 9 cm

• 7 cm

You have a right triangle with vertices at (1,1), (1,5), and (4,1). Graph the triangle and calculate the length of the hypotenuse.

• 7

• 5

• 4

• 6