Question

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

Option #1: 16

Option #2: 24

Option #3: 28

Option #4: 32

Answer 1

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**.