Answer:The length of midsegment is 34 units.
Given data:
The trapezoid KLMN, Such that KL = MN.
And , LM/KN = 8/9
Also, perimeter of KLMN = 132 units.
To find:
The length of midsegment (KM).
In the given problem, we can observe that KM is a transversal relative to parallel lines LM and KN. Which means,
Clearly, two base angles are equal. So, the triangles KLM and KMN are isosceles.
Taking the ratios of sides of two triangles as,
= KL : LM : MN : KN
= 8 : 8 : 8 : 9
The sum of ratio units is, 8 + 8 +8 +9 = 33. Then, the value of each ratio is,
Then the length of segment LM is,
And, length of segment KN is,
Then, the length of midsegment KM is obtained by taking the average of LM and KN as,
Thus, the length of midsegment is 34 units
Explanation: