← Back to the Pythagorean Theorem test
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: 8.G.B.6, 8.G.B.7 · Level: Grade 8
Question 1 Hypotenuse (2 points)
15² + 36² = 225 + 1,296 = 1,521.
√1,521 = 39.
39
Scoring: 1 point for the equation, 1 point for the answer.
Question 2 Missing leg (2 points)
b² = 37² − 12² = 1,369 − 144 = 1,225.
b = 35.
35
Scoring: 1 point for the equation, 1 point for the answer.
Question 3 Right triangles? (3 points)
(a) 11² + 60² = 121 + 3,600 = 3,721 = 61². Yes
(b) 14² + 48² = 196 + 2,304 = 2,500 = 50². Yes
(c) 9² + 12² = 81 + 144 = 225, but 16² = 256. No
Scoring: 1 point per part, with the check shown.
Question 4 Decimal sides (3 points)
x² + 2.1² = 2.9², so x² = 8.41 − 4.41 = 4.
x = 2.
x = 2.0 cm
Scoring: 1 point for the equation, 1 point for the value of x, 1 point for a correct check.
Question 5 Squares on the sides (3 points)
(a) 100 + 576 = 676
(b) √676 = 26
(c) The leg lengths are √100 = 10 and √576 = 24, so the sides 10, 24, 26 match: 10² + 24² = 676 = 26². Yes, by the converse
Scoring: 1 point per part.
Question 6 Ladder (2 points)
h² = 20² − 6² = 400 − 36 = 364.
h = √364 ≈ 19.08.
About 19.1 feet
Scoring: 1 point for the equation, 1 point for the rounded answer.
Question 7 Crate diagonal (3 points)
(a) √(6² + 3²) = √45 ≈ 6.7. About 6.7 ft
(b) d² = 36 + 9 + 4 = 49, so d = 7.
7 ft
Scoring: part (a) 1 point; part (b) 1 point for the equation, 1 point for the answer.
Question 8 Cutting the corner (2 points)
Diagonal: 40² + 96² = 1,600 + 9,216 = 10,816 and √10,816 = 104.
Along the sides: 40 + 96 = 136. Saved: 136 − 104 = 32.
32 meters
Scoring: 1 point for the diagonal, 1 point for the savings.