Gina is building the square pyramid shown below for her history class. If the length of each edge of the base is 10 inches and the height of the pyramid is 12 inches, what is the slant height of the pyramid?

A. 5 inches
Incorrect. 5 inches is half of the edge length. Where in the figure does this help to create a right triangle whose side lengths are a Pythagorean triple?

B. 12 inches
Incorrect. 12 inches is the height of the pyramid. Where in the figure does this help to create a right triangle whose side lengths are a Pythagorean triple?)

C. 13 inches
Correct! The triangle shown is a 5-12-13 right triangle.

D. 15 inches
Incorrect. Where in the figure do you see a right triangle whose side lengths could be a Pythagorean triple?

A wire is held up by two poles that are the same height on level ground, creating the isosceles trapezoid shown below. Assume that each pole is perpendicular to the ground. What is the height of each pole?

A. 3 meters
Incorrect. Find a right triangle whose side lengths are a Pythagorean triple.

B. 4 meters
Correct! The pole, diagonal portion of the wire, and a portion of the ground make a right triangle whose side lengths are a 3, 4, 5 Pythagorean triple.

C. 5 meters
Incorrect. Find a right triangle whose side lengths are a Pythagorean triple.

D. 6 meters
Incorrect. Find a right triangle whose side lengths are a Pythagorean triple.

Marcie carries a tape measure as she climbs 8 feet above the ground to the top of a slide. When she slides down the slide, she uses the tape measure to determine that the length of the metal portion of the slide is 17 feet long. What is the horizontal distance between where the bottom of the slide touches the ground and the point where she first began climbing up to the top of the slide?

A. 17 feet
Incorrect. Draw the slide as it sits on the ground. Find a right triangle whose side lengths are a Pythagorean triple.

B. 16 feet
Incorrect. Draw the slide as it sits on the ground. Find a right triangle whose side lengths are a Pythagorean triple.

C. 15 feet
Correct! The slide, along with the ground, creates a right triangle whose side lengths are an 8, 15, 17 Pythagorean triple.

D. 8 feet
Incorrect. Draw the slide as it sits on the ground. Find a right triangle whose side lengths are a Pythagorean triple.

Kenneth begins at home in Eatonton and drives 9 miles east to Latcherie. At Latcherie, he turns left to drive 40 miles north to Zwolle. What is the straight-line distance from Eatonton to Zwolle?

A. 41 miles
Correct! Eatonton, Latcherie, and Zwolle are three points that are the vertices of a right triangle whose side lengths are the Pythagorean triple 9, 40, 41.

B. 40 miles
Incorrect. Draw a map of the three towns. Find a right triangle whose side lengths are a Pythagorean triple.

C. 31 miles
Incorrect. Draw a map of the three towns. Find a right triangle whose side lengths are a Pythagorean triple.

D. 20 miles
Incorrect. Draw a map of the three towns. Find a right triangle whose side lengths are a Pythagorean triple.