$\"\"$

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The hypotenuse c = 101, length of a = 99 and length b = ?.

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Apply pythagorean theorem: $\"\"$ .

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$\"\"$ (Substitute a = 99, and c = 101)

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Evaluate powers: $\"\"$ .

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$\"\"$

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Apply subtraction property of equality: a = b then $\"\"$ .

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$\"\"$ (Subtract 9801 from each side) $\"\"$

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Apply commutative property of addition: a + b = b + a.

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$\"\"$

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Subtract: $\"\"$ )

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Apply square roots property: $\"\"$ then $\"\"$ .

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$\"\"$

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$\"\"$ (Evaluate square roots: $\"\"$ )

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The positive value of $\"\"$ $\"\"$

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The length of $\"\"$ . \ \