Answer:
[tex]8\sqrt[]{2}[/tex]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
[tex]x^2+x^2=16^2[/tex]which simplifies to give
[tex]2x^2=16^2[/tex]Dividing both sides by 2 gives
[tex]\frac{2x^2}{2}=\frac{16^2}{2}[/tex][tex]x^2=\frac{16^2}{2}[/tex]Finally, taking the square root of both sides gives
[tex]\sqrt[]{x^2}=\sqrt[]{\frac{16^2}{2}}[/tex][tex]x=\frac{16}{\sqrt[]{2}}[/tex][tex]x=8\sqrt[]{2}[/tex]which is our answer!
