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Answer:
The length of side KM is units.
Step-by-step explanation:
Given information: KLMN is a trapezoid, ∠N= ∠KML, FD=8, LM:KN=3:5, F∈ KL, D∈ MN , ME ⊥ KN KF=FL, MD=DN, .
From the given information it is noticed that the point F and D are midpoints of KL and MN respectively. The height of the trapezoid is .
Midsegment is a line segment which connects the midpoints of not parallel sides. The length of midsegment of average of parallel lines.
Since LM:KN=3:5, therefore LM is 3x and KN is 5x.
Therefore the length of LM is 6 and length of KN is 10.
Draw perpendicular on KN form L and M.
(KA=EN, isosceles trapezoid)
Therefore the length of KE is 8.
Use pythagoras theorem is triangle EKM.
Therefore the length of side KM is units.
