To find the length of the unknown side \( b \) in a right triangle with the other two sides being 24 and 12, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse (the longest side), and \( a \) and \( b \) are the other two sides. Let's assume 24 is the hypotenuse and 12 is one of the legs.
Using the theorem:
\[ 12^2 + b^2 = 24^2 \]
Calculating the squares:
\[ 144 + b^2 = 576 \]
Now, isolate \( b^2 \):
\[ b^2 = 576 - 144 \]
\[ b^2 = 432 \]
Now, take the square root to find \( b \):
\[ b = \sqrt{432} = \sqrt{144 \times 3} = 12\sqrt{3} \]
Thus, the length of the unknown side \( b \) is \( 12\sqrt{3} \), which is approximately \( 20.78 \) when calculated numerically.
If you received specific options for the answer (like those you listed), \( 12 \) and \( 24 \) are not valid answers for \( b \) since 12 is a leg and 24 is the hypotenuse. The closest numerical representation of \( 12\sqrt{3} \) in standard form is not directly listed in your options, so the exact answer is \( 12\sqrt{3} \).