Pythagorean Theorem: Geometry and Algebra Challenges

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?

• 10 feet

• 12 feet

• 14 feet

• 8 feet

A rectangular garden has a length of 10 meters and a diagonal that measures 12 meters. What is the width of the garden?

• 4√3 meters

• 8 meters

• 3 meters

• 2√11 meters

A right triangle has one leg measuring 9 cm and a hypotenuse measuring 15 cm. What is the length of the other leg?

• 10 cm

• 14 cm

• 8 cm

• 12 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 ramp is built to help wheelchair access. If the ramp is 4 feet high and 3 feet long, what is the length of the ramp?

• 6 feet

• 3 feet

• 4 feet

• 5 feet

A triangular park has one side measuring 5 meters and another side measuring 12 meters. If the park is a right triangle, what is the length of the hypotenuse?

• 14 meters

• 10 meters

• 15 meters

• 13 meters

A 20-foot tall tree casts a shadow that is 15 feet long. If you were to walk directly from the top of the tree to the end of the shadow, how far would you walk?

• 30 feet

• 20 feet

• 25 feet

• 15 feet

A right triangle has legs measuring 7 inches and 24 inches. What is the length of the hypotenuse?

• 25 inches

• 30 inches

• 26 inches

• 20 inches

A kite is flying at a height of 30 meters, and the string makes a 60-degree angle with the ground. If the string is 35 meters long, how far is the kite from the point directly below it?

• 25 meters

• 20 meters

• 30 meters

• 17.5 meters

A swimming pool is rectangular with a length of 25 meters and a width of 20 meters. What is the length of the diagonal of the pool?

• 32.015 meters

• 28.5 meters

• 35 meters

• 30 meters