Calculate Rectangle Diagonal Segment BO: Given AB=8 and AD=6

To solve this problem, we'll utilize the properties of rectangles and the Pythagorean theorem:

• Step 1: Determine the full diagonal of the rectangle using Pythagorean theorem: $AC = \sqrt{AB^2 + AD^2}$.
• Step 2: Since $O$ is the midpoint of the diagonal $AC$, $BO = \frac{AC}{2}$.

Now, let's calculate step-by-step:

Step 1: We know $AB = 8$ and $AD = 6$, therefore, using the Pythagorean theorem:

$AC = \sqrt{AB^2 + AD^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10$

Step 2: Since the diagonals bisect each other, the length of $BO$ is half of $AC$:

$BO = \frac{AC}{2} = \frac{10}{2} = 5$

Therefore, the solution to the problem is $BO = 5$.