In rectangle ADCB, we know that:
- \( DB = 26 \) (the diagonal)
- \( AB = 10 \) (one of the sides)
In a rectangle, the diagonal can be calculated using the Pythagorean theorem:
\[ DB = \sqrt{AB^2 + AD^2} \]
Here, \( AB \) is one side, and \( AD \) (which is equal to \( CB \)) is the other side. Let's denote \( AD \) (or \( CB \)) as \( x \).
According to the equation, we have:
\[ 26 = \sqrt{10^2 + x^2} \]
Squaring both sides, we get:
\[ 26^2 = 10^2 + x^2 \]
Calculating \( 26^2 \) and \( 10^2 \):
\[ 676 = 100 + x^2 \]
Now, subtract \( 100 \) from both sides:
\[ 676 - 100 = x^2 \] \[ 576 = x^2 \]
Now, take the square root of both sides:
\[ x = \sqrt{576} = 24 \]
Thus, the length of \( CB \) is \( 24 \).
The answer is Option #2: 24.
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