Given: klmn is a trapezoid, m∠n=m∠kml, fd=8, lm kn = 3 5 f∈ kl , d∈ mn , me ⊥ kn kf=fl, md=dn, me=3 5 find: km

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.