if rectangle ADCB has DB=26 and AB=10,how long is ¯¯¯¯CB¯ ?

Question

Option #1: 16
Option #2: 24
Option #3: 28
Option #4: 32

Answer 1

In rectangle ADCB, we are given that \( DB = 26 \) and \( AB = 10 \).

Since \( AB \) is parallel to \( DC \) and \( AD \) is parallel to \( BC \), the sides \( DB \) and \( AC \) are the diagonals of the rectangle.

Using the Pythagorean theorem, we can relate the sides of the rectangle to the diagonal:

\[ DB^2 = AB^2 + CB^2 \]

Substituting the values we have:

\[ 26^2 = 10^2 + CB^2 \]

Calculating \( 26^2 \) and \( 10^2 \):

\[ 676 = 100 + CB^2 \]

Now, subtract 100 from both sides:

\[ 676 - 100 = CB^2 \] \[ 576 = CB^2 \]

Finally, take the square root of both sides to find \( CB \):

\[ CB = \sqrt{576} = 24 \]

Therefore, the length of \( CB \) is \( 24 \).

So, the correct answer is Option #2: 24.