Question

mo, \\(\overline{mn}\\), and \\(\overline{on}\\) are the midsegments of \\(\triangle jkl\\). what is the perimeter of \\(\triangle jkl\\)? \\(\bigcirc\\ 6\\) \\(\bigcirc\\ 9.5\\) \\(\bigcirc\\ 11.5\\) \\(\bigcirc\\ 19\\) (diagram shows triangle (jkl) with midsegments (mo), (mn), (on); lengths (2), (3.5), (4) labeled on segments.)

Explanation:

Step1: Recall Midsegment Theorem

The Midsegment Theorem states that the midsegment of a triangle is parallel to the third side and half as long. So, if \( \overline{MO} \), \( \overline{MN} \), and \( \overline{ON} \) are midsegments, then:

• \( KL = 2 \times MN \)
• \( JK = 2 \times ON \)
• \( JL = 2 \times MO \)

Step2: Calculate each side of \( \triangle JKL \)

From the diagram:

• \( MN = 2 \), so \( KL = 2 \times 2 = 4 \)
• \( ON = 3.5 \), so \( JK = 2 \times 3.5 = 7 \)
• \( MO = 4 \), so \( JL = 2 \times 4 = 8 \)

Step3: Calculate the perimeter

Perimeter of \( \triangle JKL \) is \( JK + KL + JL \). Substitute the values:
\( 7 + 4 + 8 = 19 \)

Answer:

19