Pythagorean Theorem: 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 of the ladder reaches a height of 8 feet. Is the ladder 10 feet long?

• No, the ladder is 6 feet long.

• No, the ladder is 8 feet long.

• Yes, the ladder is 10 feet long.

• Yes, the ladder is 12 feet long.

A right triangle has one leg measuring 5 cm and the hypotenuse measuring 13 cm. What is the length of the other leg?

• 6 cm

• 10 cm

• 12 cm

• 8 cm

A rectangular park has a length of 24 meters and a width of 10 meters. If a diagonal path is built across the park, how long is the path?

• 26 meters

• 30 meters

• 22 meters

• 20 meters

A right triangle has legs measuring 9 inches and 12 inches. Verify if this triangle is a right triangle using the converse of the Pythagorean theorem.

• The triangle cannot be classified without additional information.

• Yes, the triangle is a right triangle.

• No, the triangle is not a right triangle.

• The triangle is an obtuse triangle.

A 15-foot tall tree casts a shadow that is 9 feet long. If you stand 12 feet away from the base of the tree, is the distance from you to the top of the tree a right triangle?

• No, it does not form a right triangle.

• Yes, but only if you are directly under the tree.

• No, the shadow makes it impossible to form a triangle.

• Yes, it forms a right triangle.

A triangular garden has sides measuring 7 m, 24 m, and 25 m. Determine if this garden is a right triangle using the converse of the Pythagorean theorem.

• No, the garden is not a right triangle.

• Yes, the garden is a right triangle.

• The garden has an area of 168 m².

• The garden is an equilateral triangle.

A right triangle has a hypotenuse of 10 cm and one leg of 6 cm. Calculate the length of the other leg.

• 8 cm

• 5 cm

• 9 cm

• 7 cm

A ramp is built to help wheelchair access. If the ramp is 4 feet long and rises 3 feet, is the base of the ramp less than 2.5 feet?

• Yes

• No

• The base is exactly 2.5 feet

• The base is 3 feet

A right triangle has one leg measuring 8 feet and a hypotenuse measuring 10 feet. What is the length of the other leg?

• 6 feet

• 8 feet

• 10 feet

• 4 feet

A 30-foot tall building casts a shadow of 40 feet. If you stand 50 feet away from the base of the building, is the distance from you to the top of the building a right triangle?

• Yes

• No, the shadow creates a triangle.

• Yes, but only if you are directly under the building.

• No, the distance forms a circle.