Answer:
12√3
Explanation:
First, we know that JL = 24.
Then, the triangle JKL is equilateral. It means that all the sides are equal, so JK is also equal to 24.
Finally, N is the midpoint of segment JK, so it divides the segment JK into two equal parts. Therefore, JN = 12.
Now, we have a right triangle JLN, where JL = 24 and JN = 12.
Then, we can use the Pythagorean theorem to find the third side of the triangle, so NL is equal to:
[tex]\begin{gathered} NL=\sqrt[]{(JL)^2-(JN)^2} \\ NL=\sqrt[]{24^2-12^2} \end{gathered}[/tex]
Because JL is the hypotenuse of the triangle and JN and NL are the legs.
So, solving for NL, we get:
[tex]\begin{gathered} NL=\sqrt[]{576-144} \\ NL=\sqrt[]{432} \\ NL=\sqrt[]{144(3)} \\ NL=\sqrt[]{144}\cdot\sqrt[]{3} \\ NL=12\sqrt[]{3} \end{gathered}[/tex]
Therefore, the length of NL is 12√3
