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

Tags

CCSS.8.G.B.8

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

Tags

CCSS.8.G.B.8

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

Tags

CCSS.8.G.B.7

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

Tags

CCSS.8.G.B.8

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.

Tags

CCSS.8.G.B.8

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

Tags

CCSS.8.G.B.8

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

Tags

CCSS.8.G.B.8

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

Tags

CCSS.8.G.B.7

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

Tags

CCSS.8.G.B.8

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

Tags

CCSS.8.G.B.7