Question

the midsegment of \\( \triangle abc \\) is \\( \overline{lm} \\). what is the length of \\( \overline{ac} \\) if \\( \overline{lm} \\) is 12 inches long?
a. 6 inches
b. 24 inches
c. 30 inches
d. 15 inches

Explanation:

Step1: Recall the midsegment theorem

The midsegment of a triangle is parallel to the third side and half its length.

Step2: Apply the theorem

Let \( LM \) be the midsegment and \( AC \) be the third side. By the midsegment theorem, \( LM=\frac{1}{2}AC \). Given \( LM = 12\) inches. Then \( AC=2\times LM\).

Step3: Calculate the length of \( AC \)

Substitute \( LM = 12\) into the formula \( AC = 2\times LM\). So \( AC=2\times12=24\) inches.

Answer:

B. 24 inches