Question

Given:• AJKL is an equilateral triangle.• N is the midpoint of JK.• JL 24.What is the length of NL?L24JKNO 12O 8V3O 12V2O 1213

Answer 1

12√3

Step-by-step 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:

`\begin{gathered} NL=\sqrt[]{(JL)^2-(JN)^2} \\ NL=\sqrt[]{24^2-12^2} \end{gathered}`

Because JL is the hypotenuse of the triangle and JN and NL are the legs.

So, solving for NL, we get:

`\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}`

Therefore, the length of NL is 12√3