Final answer:
The midsegment (LM) of a triangle is half the length of the corresponding side (AC), thus if AC is 26 inches, LM would be half of that, which is 13 inches.
Step-by-step explanation:
The midsegment of a triangle (also known as the midline or mid-segment) is a line segment connecting the midpoints of two sides of the triangle. In this question, segment LM is the midsegment of △ABC, and we are looking to find its length given that side AC is 26 inches long. According to the properties of a triangle's midsegment, it is parallel to the third side and half its length. Since AC is 26 inches long, and LM is the midsegment parallel to AC, the length of LM is therefore half of AC.
The length of LM is calculated as follows: LM = ½ × AC = ½ × 26 inches = 13 inches. So, the length of the midsegment LM is 13 inches.