8th Grade Pythagorean Theorem: Triangle Types & Problems

A ladder is leaning against a wall. The foot of the ladder is 6 feet from the wall, and the ladder reaches a height of 8 feet. Is the triangle formed by the ladder, the wall, and the ground a right triangle?

• Yes, it is a right triangle.

• Yes, it is an acute triangle.

• No, it is an obtuse triangle.

• No, it is a scalene triangle.

A triangular park has sides measuring 5 meters, 12 meters, and 13 meters. Determine if this park is a right triangle and explain your reasoning using the Pythagorean theorem.

• No, the park is not a right triangle because the sides do not satisfy the Pythagorean theorem.

• No, the park is a right triangle but not according to the Pythagorean theorem.

• Yes, the park is a right triangle.

• Yes, but only if the longest side is 12 meters.

A rectangular garden has a length of 10 meters and a width of 24 meters. If you want to plant a diagonal path from one corner to the opposite corner, how long will the path be?

• 26 meters

• 30 meters

• 20 meters

• 22 meters

A right triangle has one leg measuring 9 cm and the other leg measuring 12 cm. Calculate the length of the hypotenuse and determine the type of triangle formed by these sides.

• The length of the hypotenuse is 20 cm and it is an obtuse triangle.

• The length of the hypotenuse is 10 cm and it is a scalene triangle.

• The length of the hypotenuse is 13 cm and it is an isosceles triangle.

• The length of the hypotenuse is 15 cm and it is a right triangle.

A baseball diamond is a square with each side measuring 90 feet. What is the distance from home plate to second base? Is this distance a hypotenuse of a right triangle?

• 90√2 feet

• 45√2 feet

• 180 feet

• 90 feet

A right triangle has a hypotenuse of 15 cm and one leg measuring 9 cm. Find the length of the other leg and classify the triangle based on its side lengths.

• The length of the other leg is 10 cm and the triangle is isosceles.

• The length of the other leg is 12 cm and the triangle is scalene.

• The length of the other leg is 6 cm and the triangle is right-angled.

• The length of the other leg is 8 cm and the triangle is equilateral.

A ramp is built to help wheelchair access to a building. If the ramp is 10 feet long and rises 4 feet, is the ramp steep enough to form a right triangle?

• No, the ramp only rises 2 feet.

• Yes, the ramp is steep enough to form a right triangle.

• Yes, but it is not steep enough for wheelchair access.

• No, the ramp is too short to form a right triangle.

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

• 30 meters

• 60 meters

• 20 meters

• 40 meters

A right triangle has angles measuring 90 degrees, 60 degrees, and 30 degrees. If the shortest side is 5 cm, find the lengths of the other two sides and confirm the triangle type.

• 10 cm and 5√2 cm

• 5 cm and 15 cm

• The lengths of the other two sides are 5√3 cm and 10 cm.

• 7 cm and 12 cm