Mastering Pythagorean Theorem in Right Triangles

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. Is the ladder 10 feet long?

• Yes, the ladder is 10 feet long.

• No, the ladder is 6 feet long.

• Yes, the ladder is 12 feet long.

• No, the ladder is 8 feet long.

A right triangle has one leg measuring 5 cm and the other leg measuring 12 cm. What is the length of the hypotenuse?

• 13 cm

• 15 cm

• 10 cm

• 14 cm

A 45-45-90 triangle has legs that are each 7 inches long. What is the length of the hypotenuse?

• 14 inches

• 7 inches

• 10 inches

• 7√2 inches

A triangular park has a height of 9 meters and a base of 12 meters. If the park is shaped like a right triangle, what is the length of the hypotenuse?

• 10 meters

• 15 meters

• 12 meters

• 18 meters

A 30-60-90 triangle has a shorter leg of 4 meters. What is the length of the longer leg and the hypotenuse?

• Longer leg: 8 meters, Hypotenuse: 4√3 meters

• Longer leg: 6 meters, Hypotenuse: 10 meters

• Longer leg: 4√3 meters, Hypotenuse: 8 meters

• Longer leg: 4 meters, Hypotenuse: 4√3 meters

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

• 12 cm

• 8 cm

• 6 cm

A ramp is built to help wheelchair access. If the ramp is 10 feet long and rises 6 feet, how far is the base of the ramp from the wall?

• 8 feet

• 5 feet

• 12 feet

• 10 feet

A right triangle has one leg that is 8 inches long and a hypotenuse that is 10 inches long. What is the length of the other leg?

• 6 inches

• 10 inches

• 8 inches

• 4 inches

A 30-60-90 triangle has a hypotenuse of 16 cm. What are the lengths of the other two sides?

• Shorter leg: 12 cm, Longer leg: 12 cm

• Shorter leg: 5 cm, Longer leg: 15 cm

• Shorter leg: 10 cm, Longer leg: 6 cm

• Shorter leg: 8 cm, Longer leg: 8√3 cm (approximately 13.86 cm)

A right triangle has legs measuring 9 cm and 12 cm. What is the area of the triangle?

• 36 cm²

• 72 cm²

• 45 cm²

• 54 cm²