Pythagorean Theorem Test – Grade 8 Math (Printable PDF)

Question 1 Hypotenuse (2 points)

Two legs of a right triangle measure 15 and 36. How long is the hypotenuse?

Question 2 Missing leg (2 points)

The hypotenuse of a right triangle is 37 and one leg is 12. What is the length of the other leg?

Question 3 Right triangles? (3 points)

For each list of side lengths, decide whether a right triangle is possible and show the check.

1. 11, 60, 61 (1 point)
2. 14, 48, 50 (1 point)
3. 9, 12, 16 (1 point)

Question 4 Decimal sides (3 points)

Find x in the right triangle. Show the equation and check your answer.

Question 5 Squares on the sides (3 points)

The squares built on the legs of a right triangle have areas 100 and 576.

1. Find the area of the square on the hypotenuse. (1 point)
2. Find the length of the hypotenuse. (1 point)
3. Is a triangle with sides 10, 24, and 26 a right triangle? Explain. (1 point)

Question 6 Ladder (2 points)

A 20-foot ladder leans against a wall with its base 6 feet from the wall. How high up the wall does it reach? Round to the nearest tenth of a foot.

Question 7 Crate diagonal (3 points)

A crate is 6 feet long, 3 feet wide, and 2 feet tall.

1. Find the diagonal of the base to the nearest tenth of a foot. (1 point)
2. Find the length of the longest pole that fits inside the crate. (2 points)

Question 8 Cutting the corner (2 points)

A rectangular field is 40 meters by 96 meters. A student walks along the diagonal instead of along two sides. How many meters does the shortcut save?