Question

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

Explanation:

Step1: Use the midsegment theorem

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

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

The perimeter \(P\) of \(\triangle JKL\) is \(P=JK + KL+JL\).
Substitute the values: \(P = 7+4 + 8\).

$$P=19$$

Answer:

19