Question

what is the length of mn?
58 cm
75 cm
88 cm
116 cm

Explanation:

Step1: Identify the mid - segment theorem

In a triangle, the mid - segment (a segment connecting the mid - points of two sides of a triangle) is parallel to the third side and half its length. Here, \(M\) is the mid - point of \(AB\) (\(AM = MB\)) and \(N\) is the mid - point of \(BC\) (\(BN=NC\)), so \(MN\) is a mid - segment of \(\triangle ABC\).

Step2: Apply the mid - segment formula

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

$$MN=\frac{1}{2}\times116$$

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

Answer:

58 cm