Question

Urgent Help needed w/ right triangle trig

Answer 1

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.

${c}^{2} = {a}^{2} + {a}^{2} \\ \\ {c}^{2} = 2 {a}^{2}$
Now taking square root on both side we get ;

$c = \sqrt{2} a$
Now pluging the value of C in the above equation we get ;

$12 = \sqrt{2} a \\ \\ a = \frac{12}{ \sqrt{2} } = 6 \sqrt{2}$
Therefore LP = 6√2 units.