we can use the pythagorean theorem to find the length of PN in triangle OPN
a²+b²=c²
where a and b are legs and c is the hypotenuse
we are given one leg (OP=8) and the hypotenuse (ON=18) so now we can plug in these numbers to find PN
8²+b²=18²
64+b²=324
b²=260
b=√260
b=√4 * √65
b=2√65
now that we have the value of PN, we can get the value of LN by doubling 2√65
2(2√65) = 4√65
so your answer should be:
LN = 4√65
hope this helped
