Question

mo, mn, and on are the midsegments of △jkl. what is the perimeter of △jkl? 6 9.5 11.5 19

Explanation:

Step1: Apply the mid - segment theorem

The mid - segment of a triangle is parallel to the third side and half its length.
If \(MO\) is a mid - segment, then \(JL = 2\times MO\). If \(MN\) is a mid - segment, then \(KL=2\times MN\). If \(ON\) is a mid - segment, then \(JK = 2\times ON\).

Step2: Calculate the lengths of the sides of \(\triangle JKL\)

Given \(MO = 3.5\), \(MN = 2\), \(ON = 4\)
\(JL=2\times3.5 = 7\), \(JK = 2\times4=8\), \(KL=2\times2 = 4\)

Step3: Calculate the perimeter of \(\triangle JKL\)

The perimeter \(P\) of \(\triangle JKL\) is \(P=JK + KL+JL\)
\(P=8 + 4+7=19\)

Answer:

19