Geometry and Trigonometry practice question

Answer: A. 5, 12, 13

Three lengths form a right triangle exactly when the two shorter ones satisfy a² + b² = c² with the longest as c. Check: 5² + 12² = 25 + 144 = 169 = 13². None of the other sets works.

Why the other answers are wrong

B. 4, 5, 6

4² + 5² = 16 + 25 = 41, but 6² = 36. Consecutive whole numbers don't make a right triangle here.

C. 7, 8, 9

7² + 8² = 49 + 64 = 113, but 9² = 81. The squares of the two shorter sides must add to the square of the longest.

D. 3, 4, 6

3, 4 and 5 would work — but the longest side here is 6, and 3² + 4² = 25 while 6² = 36.

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