Pythagorean Challenges: Calculate Distances & Triples

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. How long is the ladder?

• 12 feet

• 14 feet

• 8 feet

• 10 feet

A rectangular park has a length of 30 meters and a width of 40 meters. What is the distance from one corner of the park to the opposite corner?

• 20 meters

• 60 meters

• 50 meters

• 70 meters

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

• 15 cm

• 17 cm

• 13 cm

• 10 cm

Two buildings are 50 meters apart. One building is 30 meters tall, and the other is 40 meters tall. What is the distance between the tops of the two buildings?

• 10√26 meters (approximately 101.0 meters)

• 60 meters

• 50 meters

• 70 meters

A right triangle has sides of lengths 5, 12, and 13. Verify if this is a Pythagorean triple and explain why it is or isn't.

• It is a Pythagorean triple, but the longest side is not 13.

• Yes, but it is not a right triangle due to the side lengths.

• Yes, it is a Pythagorean triple.

• No, it is not a Pythagorean triple because the sides do not satisfy the equation.

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

• 90√2 feet

• 45√2 feet

A 15-foot tall tree casts a shadow that is 9 feet long. How far is the tip of the shadow from the base of the tree?

• 9 feet

• 12 feet

• 8 feet

• 10 feet

A right triangle has legs measuring 8 inches and 15 inches. Calculate the length of the hypotenuse.

• 17 inches

• 12 inches

• 20 inches

• 10 inches

A 20-foot long ramp is used to load a truck. If the base of the ramp is 16 feet from the truck, how high does the ramp reach?

• 8 feet

• 14 feet

• 10 feet

• 12 feet

A right triangle has one leg measuring 7 cm and a hypotenuse measuring 25 cm. What is the length of the other leg?

• 20 cm

• 15 cm

• 10 cm

• 24 cm