is (5,12,13) a pythagorean triple?

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Solution

Dear Student,
$P y t h a g o r e a n t r i p l e t m e a n s s u m o f s q u a r e o f t w o s i d e s o f t r i a n g l e = s q u a r e o f t h i r d s i d e S o, 5^{2} + 12^{2} = 13^{2} 25 + 144 = 13^{2} 169 = 13^{2} 13^{2} = 13^{2} h e n c e (5, 12, 13) a p y t h a g o r e a n t r i p l e$
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