Question

what is the length of (overline{mn})?
58 cm
75 cm
88 cm
116 cm

Explanation:

Step1: Recall the mid - segment theorem

The mid - segment of a triangle is parallel to the third side and half its length. In \(\triangle ABC\), \(M\) is the mid - point of \(AB\) (since \(AM = MB\)) and \(N\) is the mid - point of \(BC\) (since \(BN=NC\)). So, \(MN\) is the mid - segment of \(\triangle ABC\) with respect to side \(AC\).

Step2: Apply the mid - segment formula

The formula for the length of the mid - segment \(MN\) is \(MN=\frac{1}{2}AC\). Given \(AC = 116\mathrm{cm}\), then \(MN=\frac{1}{2}\times116\).

$$MN = 58\mathrm{cm}$$

Answer:

58 cm