Which of these is NOT a Pythagorean triple?

Class 7The Triangle and its PropertiesTriangles

A9, 12, 15
B9, 12, 16
C8, 15, 17
D12, 35, 37

Step-by-Step Solution

9^{2} + 1 2^{2} = 81 + 144 = 225

. That equals

1 5^{2}

(225) but not

1 6^{2}

(256), so 9, 12, 16 fails. The others hold:

8^{2} + 1 5^{2} = 64 + 225 = 289 = 1 7^{2}

, and

1 2^{2} + 3 5^{2} = 144 + 1225 = 1369 = 3 7^{2}

. Trap: the first two options differ by one unit in the largest number, so only squaring — not eyeballing — settles it.

Answer: B) 9, 12, 16

Key idea: Pythagoras theorem (right triangles only)

In a **right** triangle, the square of the hypotenuse equals the sum of the squares of the other two sides:

hypotenus

e^{2}

= side₁² + side₂²

Classic Pythagorean triple: 3, 4, 5 — because

3^{2} + 4^{2} = 9 + 16 = 25 = 5^{2}

.

Other triples to recognise: (5, 12, 13), (8, 15, 17), (7, 24, 25). The rule only applies when one of the angles is 90°. Never use Pythagoras for non-right triangles.

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