It is clearly understood from the image that LPNM is a square.
Let the side of the square be 'a' units.
Then by Pythagorean theorem.
[tex] {c}^{2} = {a}^{2} + {a}^{2} \\ \\ {c}^{2} = 2 {a}^{2} [/tex]
Now taking square root on both side we get ;
[tex]c = \sqrt{2} a[/tex]
Now pluging the value of C in the above equation we get ;
[tex]12 = \sqrt{2} a \\ \\ a = \frac{12}{ \sqrt{2} } = 6 \sqrt{2} [/tex]
Therefore LP = 6√2 units.
