\"\"

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The give side measures are 30, 40, 50.

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Since the measure of the longest side is 50, So let c = 50, a = 30 and b = 40.

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Then apply Pythagorean theorem: \"\".

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\"\"           (Substitute c = 50, a = 30 and b = 40)\"\"

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Evaluate powers: \"\".

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\"\"

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\"\"

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Since \"\", the triangle is right triangle.\"\"

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The measures \"\", the triangle is right triangle.