It seems you are providing a few numerical values (38, 9, x) followed by the Pythagorean theorem \( a^2 + b^2 = c^2 \). If you're looking for a relationship between the numbers and the Pythagorean theorem, let's analyze this step-by-step:
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Pythagorean Theorem: This theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).
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Identifying Values: Let's assign the values you provided to \( a \), \( b \), and \( c \):
- Let \( a = 9 \)
- Let \( c = 38 \)
- Then, we need to find \( b \) (where \( b = x \)).
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Using the Theorem: \[ a^2 + b^2 = c^2 \] Substituting the values: \[ 9^2 + x^2 = 38^2 \]
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Calculating: \[ 81 + x^2 = 1444 \] \[ x^2 = 1444 - 81 \] \[ x^2 = 1363 \] \[ x = \sqrt{1363} \approx 36.9 \]
So \( x \approx 36.9 \) and it fits into the context of the Pythagorean theorem as one of the legs of a right triangle alongside the other provided values.