Answer:
Length of KM is:
80 units
Step-by-step explanation:
since, line a is a perpendicular bisector of KM
this implies that:
∠NLM=∠NLK=90°
and KL=LM
By SAS property, ΔNLK and ΔNLm are similar
(NL side is common in both, ∠NLK=∠NLM and KL=LM)
Hence, [tex]\dfrac{NK}{NM}=\dfrac{KL}{LM}\\\\\\\dfrac{9x-5}{7x+7}= \dfrac{6x+4}{6x+4} \\\\\\\dfrac{9x-5}{7x+7}=1\\ \\\\9x-5=7x+7\\\\x=6[/tex]
Hence, Length of KM=KL+LM
=6x+4+6x+4
=12x+8
=12×6+8
= 80 units
