Answer: 24 unit
Explanation:
Here, MNOK is a trapezoid, MN=OK, m∠M=60°, NK ⊥ MN , MK=16cm
Since, a mid segment is the line segment which joins the mid points of the equal sides of the isosceles trapezoid.
Let LO is the mid segment of trapezoid MNOK
Where, Let J is the intersection point of KN and LO.
Therefore, LO= LJ+JO --------(1)
And, KL=LO , MO=ON
Since, In triangle KLJ,
∠LKJ=90° ( given), ∠KLJ=60° ( because, LO║ON and it is given m∠M=60°)
Thus, ∠KJL=30°
Therefore, sin 30°=LK/LJ=8/LJ ( Because ΔMKN is a isoceleus triangle where ∠MKN=∠MNK=30°⇒KM=MN)
⇒LJ=8×2=16
Now, In ΔNOJ,
∠ONJ=∠OJN=30°
Therefore, ON=OJ ( by the property of isosceles triangle)
⇒OJ=8
Thus, By putting these values in equation 1) we get,
LO=16+8=24 cm