Pythagorean Challenges: Radical Geometry Word Problems

A ladder is leaning against a wall. The base 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?

• 8 feet

• 12 feet

• 14 feet

• 10 feet

A rectangular garden measures 10 meters by 24 meters. If you want to plant a diagonal flower bed from one corner to the opposite corner, how long will the flower bed be?

• 20 meters

• 30 meters

• 22 meters

• 26 meters

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

• 13 cm

• 10 cm

• 15 cm

• 17 cm

A square park has a side length of 14 meters. What is the distance from one corner of the park to the opposite corner?

• 14 meters

• 28 meters

• 14√2 meters

• 7√2 meters

A triangular piece of land has sides measuring 5 meters, 12 meters, and 13 meters. Is this triangle a right triangle?

• No, this triangle is not a right triangle.

• Yes, this triangle is an equilateral triangle.

• No, this triangle is an obtuse triangle.

• Yes, this triangle is a right triangle.

A swimming pool is 15 feet long and 20 feet wide. If you want to place a diving board diagonally across the pool, how long will the diving board need to be?

• 20 feet

• 30 feet

• 15 feet

• 25 feet

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

• 9 cm

• 8 cm

• 7 cm

• 5 cm

A square tile has a side length of 8 inches. What is the length of the diagonal of the tile?

• 11.31 inches

• 10 inches

• 9.5 inches

• 12 inches

A right triangle has legs measuring 7 inches and 24 inches. Calculate the length of the hypotenuse and round it to the nearest whole number.

• 20

• 30

• 22

• 25

A rectangular field is 30 meters long and 40 meters wide. What is the distance from one corner of the field to the opposite corner?

• 50 meters

• 30 meters

• 70 meters

• 40 meters