Question

applying the triangle midsegment theorem
\\( \overline { mo } , \overline { mn } \\), and \\( \overline { on } \\) are the midsegments of \\( \triangle jkl \\).
what is the perimeter of \\( \triangle jkl \\)?
6
9.5
11.5
19

Explanation:

Step1: Use the triangle midsegment theorem

The triangle midsegment theorem states that a midsegment of a triangle is parallel to the third side and half its length.
So, if \(MO = 2\), then \(KL=2\times MO = 4\); if \(MN = 4\), then \(JL = 2\times MN=8\); if \(ON = 3.5\), then \(JK=2\times ON = 7\).

Step2: Calculate the perimeter of \(\triangle JKL\)

The perimeter \(P\) of \(\triangle JKL\) is \(P=JK + KL+JL\).
Substitute \(JK = 7\), \(KL = 4\), and \(JL = 8\) into the formula: \(P=7 + 4+8=19\).

Answer:

\(19\)