Question

Given: KLMN is a trapezoid, KL=MN, m∠1=m∠2, LM/KN = 8/9 , Perimeter KLMN=132 Find: The length of midsegment.

Answer 1

Answer:

34

Step-by-step explanation:

KM is a transversal relative to parallel lines LM and KN. Thus ∠2 = ∠MKN ≅ ∠KML and ∠KML = ∠1. The two base angles of ΔKLM are equal, so that triangle is isosceles.

Then the ratios of all the sides are ...

... KL : LM : MN : KN = 8 : 8 : 8 : 9

The sum of these ratio units is 33, so each one stands for 132/33 = 4 perimeter length units. Then segment LM is 8×4 = 32 perimeter length units, and KN is 9×4 = 36 permeter length units.

The midsegment is the average of lengths LM and KN, so is ...

... (32 +36)/2 = 34 . . . . perimeter length units