Pythagorean Challenges: Find Missing Sides & Verify Triangles

A ladder is leaning against a wall. The foot of the ladder is 6 feet away from the wall, and the top reaches a height of 8 feet. Is the ladder longer than 10 feet?

• Yes, the ladder is exactly 10 feet long.

• No

• The ladder is 12 feet long.

• The ladder is 9 feet long.

A triangular park has sides measuring 5 meters, 12 meters, and 13 meters. Can you determine if this park is a right triangle?

• No, the park is a scalene triangle.

• No, the park is an obtuse triangle.

• Yes, the park is a right triangle.

• Yes, the park is an equilateral triangle.

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

• 8 cm

• 12 cm

• 14 cm

• 10 cm

A rectangular garden has a diagonal of 10 meters and one side measuring 6 meters. What is the length of the other side?

• 5 meters

• 8 meters

• 9 meters

• 7 meters

A right triangle has legs measuring 7 inches and 24 inches. Calculate the length of the hypotenuse. Is it a right triangle?

• 20 inches, yes, it is a right triangle.

• 30 inches, yes, it is a right triangle.

• 25 inches, yes, it is a right triangle.

• 26 inches, no, it is not a right triangle.

A right triangle has a hypotenuse of 25 cm and one leg of 20 cm. What is the length of the other leg?

• 10 cm

• 30 cm

• 20 cm

• 15 cm

A 30-foot tall tree casts a shadow of 18 feet. Is the tree taller than 25 feet based on the Pythagorean theorem?

• Yes, the tree is taller than 25 feet.

• The tree's height cannot be determined from the shadow.

• The tree is exactly 25 feet tall.

• No, the tree is shorter than 20 feet.

A right triangle has sides measuring 8 cm, 15 cm, and 17 cm. Verify if it is a right triangle using the converse of the Pythagorean theorem.

• The triangle is right-angled but not valid.

• Yes, it is a right triangle.

• No, it is not a right triangle.

• It could be a right triangle if the sides were different.

A ramp is built to help wheelchair access. If the ramp is 12 feet long and rises 5 feet, is the ramp steep enough to be considered safe?

• The ramp is too short to determine safety.

• No, the ramp is too steep to be considered safe.

• Yes, the ramp is safe and accessible.

• The ramp is safe for all users.