Question

triangle nop is formed by connecting the midpoints of the side of triangle klm. the lengths of the sides of triangle nop are shown. what is the length of \\( \overline { l m } \\)? figures not necessarily drawn to scale.

Explanation:

Step1: Use the mid - segment theorem

The mid - segment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.
In triangle \(KLM\), since \(NOP\) is formed by connecting the midpoints of the sides of triangle \(KLM\), the side \(LM\) is twice the length of the side \(OP\) (where \(OP = 8\)).

Step2: Calculate the length of \(LM\)

Let \(LM=x\). According to the mid - segment theorem \(x = 2\times8\).

Answer:

\(16\)