Answer:
![8\sqrt[]{2}](https://img.qammunity.org/2023/formulas/mathematics/college/ok50jtlpz2gsyecq8nva4z9em3ybls8dpj.png)
Step-by-step explanation:
The triangle formed by the wooden bracket and the sides is shown below
The distance labeled x is the distance from the corner.
Note that the vertical side and the horizontal sides are both X away from the corner as demanded.
Now, the Pythagorean theorem says that

which simplifies to give

Dividing both sides by 2 gives


Finally, taking the square root of both sides gives
![\sqrt[]{x^2}=\sqrt[]{(16^2)/(2)}](https://img.qammunity.org/2023/formulas/mathematics/college/8ch117l4hbjl44vo634d0599w1xevpfcam.png)
![x=\frac{16}{\sqrt[]{2}}](https://img.qammunity.org/2023/formulas/mathematics/college/gon0gorddco4un22wked0de3kjstvv1ohx.png)
![x=8\sqrt[]{2}](https://img.qammunity.org/2023/formulas/mathematics/college/ea9kev8hmxm71y072m5vme7cnl1r3yxhbk.png)
which is our answer!