A triangle has sides $9$, $12$, $15$. Is it a right-angled triangle?

A triangle has sides $9$, $12$, $15$. Is it a right-angled triangle?
  1. Yes
  2. No
  3. Cannot determine
  4. It is equilateral

Solution

$9^{2} + 12^{2} = 81 + 144 = 225 = 15^{2}$. So it is right-angled (with hypotenuse $15$).

Asked in: IMO

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