To find the length of the second side of the right triangle, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \(c\) is the length of the hypotenuse and \(a\) and \(b\) are the lengths of the other two sides. Here, we know:
- \(c = 13\)
- \(a = 5\)
- \(b = ?\)
Plugging the known values into the equation:
\[ 5^2 + b^2 = 13^2 \]
Calculating \(5^2\) and \(13^2\):
\[ 25 + b^2 = 169 \]
Now, isolate \(b^2\) by subtracting 25 from both sides:
\[ b^2 = 169 - 25 \] \[ b^2 = 144 \]
Taking the square root of both sides gives us:
\[ b = \sqrt{144} = 12 \]
Therefore, the length of the second side is 12.
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