Pythagorean Triples: Solve Problems & Calculate Lengths

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. Is the length of the ladder a Pythagorean triple? Calculate the length of the ladder.

• 8 feet

• 14 feet

• 10 feet

• 12 feet

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

• 13 cm, yes, it is a Pythagorean triple.

• 10 cm, no, it is not a Pythagorean triple.

• 15 cm, yes, it is a Pythagorean triple.

• 14 cm, no, it is not a Pythagorean triple.

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

• 30 meters

• 20 meters

• 15 meters

• 25 meters

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

• 5 + 12 * √3 feet, approximately 21.78 feet

• 10 feet

• 15 feet

• 18 feet

A right triangle has sides of lengths 7 cm and 24 cm. Calculate the length of the hypotenuse and determine if these lengths form a Pythagorean triple.

• The length of the hypotenuse is 25 cm, and these lengths form a Pythagorean triple.

• The length of the hypotenuse is 26 cm, and these lengths do not form a Pythagorean triple.

• The length of the hypotenuse is 20 cm, and these lengths form a Pythagorean triple.

• The length of the hypotenuse is 30 cm, and these lengths 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?

• 45√2 feet

• 90 feet

• 90√2 feet

• 180 feet

A ramp is built to help wheelchair access to a building. If the ramp rises 4 feet and extends 3 feet horizontally, what is the length of the ramp? Is this a Pythagorean triple?

• 5 feet, yes

• 7 feet, yes

• 4 feet, no

• 6 feet, yes

A right triangle has a hypotenuse of 13 cm and one leg measuring 5 cm. Calculate the length of the other leg and check if the sides form a Pythagorean triple.

• 10 cm

• 15 cm

• 8 cm

• 12 cm

A 30-foot tall flagpole casts a shadow that is 40 feet long. How far is the base of the flagpole from the tip of the shadow?

• 60 feet

• 40 feet

• 30 feet

• 50 feet

A right triangle has legs measuring 8 inches and 15 inches. What is the length of the hypotenuse, and does it form a Pythagorean triple?

• 20 inches, no

• 18 inches, yes

• 16 inches, no

• 17 inches, yes