To find \( x \) using the Pythagorean theorem, we can set up our equation based on a right triangle. The theorem states that in a right triangle, the square of the length of the hypotenuse \( c \) is equal to the sum of the squares of the lengths of the other two sides \( a \) and \( b \):
\[ c^2 = a^2 + b^2 \]
If we can set up specific values for \( a \), \( b \), and \( c \), we can solve for \( x \).
From the information provided:
- The choices include:
- x = 1698
- x = \frac{169}{8}
- x = 16912
- x = \frac{169}{12}
- x = \frac{169}{144}
- x = 12, 13, and 5
- Assuming \( 12 \), \( 13 \), and \( 5 \) are the sides of a right triangle:
- Let \( a = 5 \) and \( b = 12 \), so we calculate \( c \):
\[ c^2 = 5^2 + 12^2 \] \[ c^2 = 25 + 144 \] \[ c^2 = 169 \] \[ c = \sqrt{169} = 13 \]
The values \( 5 \), \( 12 \), and \( 13 \) do indeed form a Pythagorean triple.
Thus, it seems like a comparison of values is needed. It suggests we check for \( x \) being equal to pairs of (12, 13, and 5) instead of specific values like \( \frac{169}{8} \) or \( \frac{169}{144} \).
Since none of the other fractions seem to be defined in this context with Pythagorean triplets, the answer appears to be:
x = 12, 13, and 5 are valid sides of a right triangle based on the Pythagorean theorem.
3 answers