Real-World Pythagorean Challenges for Grade 8

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 on the wall. How long is the ladder?

• 12 feet

• 8 feet

• 14 feet

• 10 feet

A rectangular park has a length of 30 meters and a width of 40 meters. What is the distance between two opposite corners of the park?

• 60 meters

• 70 meters

• 40 meters

• 50 meters

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

• 10 cm

• 13 cm

• 17 cm

• 15 cm

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

• 90 feet

• 90√2 feet

• 180 feet

• 45√2 feet

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

• 15 feet

• Approximately 17.44 feet

• 12.5 feet

• 20 feet

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

• 10 cm

• 6 cm

• 12 cm

• 8 cm

A ramp is built to help wheelchair access. If the ramp is 4 feet long and rises 3 feet high, how far is the base of the ramp from the wall it is leaning against?

• 4.5 feet

• 3.5 feet

• 1.5 feet

• Approximately 2.65 feet

A kite is flying at a height of 50 meters. If the string is 80 meters long, how far is the kite from the point on the ground directly below it?

• 62.45 meters

• 80 meters

• 30 meters

• 50 meters

A swimming pool is in the shape of a rectangle. If the length is 20 meters and the width is 15 meters, what is the diagonal distance across the pool?

• 15 meters

• 30 meters

• 20 meters

• 25 meters

A right triangle has a hypotenuse of 10 inches and one leg of 6 inches. What is the length of the other leg?

• 5 inches

• 8 inches

• 7 inches

• 9 inches