Real-Life Pythagorean Problems for 8th Graders

A ladder is leaning against a wall. The base of the ladder is 4 feet away from the wall, and the ladder reaches a height of 3 feet on the wall. How long is the ladder?

• 4 feet

• 6 feet

• 3.5 feet

• 5 feet

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

• 45 meters

• 55 meters

• 60 meters

• 50 meters

A right triangle has one leg measuring 6 cm and the other leg measuring 8 cm. What is the length of the hypotenuse?

• 12 cm

• 8 cm

• 14 cm

• 10 cm

A soccer field is in the shape of a rectangle. If the length is 50 meters and the width is 30 meters, what is the distance from one corner of the field to the opposite corner?

• 58.31 meters

• 70 meters

• 55 meters

• 45 meters

A tree casts a shadow that is 10 feet long. If the top of the tree is 15 feet high, how far is the base of the tree from the end of the shadow?

• 18.03 feet

• 15 feet

• 12.5 feet

• 20 feet

A ramp is built to help wheelchair access. If the ramp is 12 feet long and rises 5 feet high, how far is the base of the ramp from the wall it is leaning against?

• 12 feet

• 6 feet

• 10.91 feet

• 8.5 feet

A swimming pool is rectangular with a length of 20 meters and a width of 15 meters. What is the length of the diagonal across the pool?

• 30 meters

• 25 meters

• 15 meters

• 20 meters

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

• 12 cm

• 10 cm

• 8 cm

• 6 cm

A kite is flying at a height of 30 meters. If the string of the kite is 50 meters long, how far is the kite from the point on the ground directly below it?

• 30 meters

• 40 meters

• 20 meters

• 60 meters

A construction worker needs to place a support beam diagonally across a rectangular frame that is 9 feet wide and 12 feet tall. What is the length of the support beam?

• 12 feet

• 10 feet

• 18 feet

• 15 feet