Question

solving for an unknown segment length
what is the length of segment lm?
units

Explanation:

Step1: Set up the equation

Since \(NK = NM\) (given by the marks on the segments), we have \(14x - 3=25\).
Solve for \(x\):
\(14x=25 + 3\)
\(14x=28\)
\(x = 2\)

Step2: Find the length of \(KL\)

Substitute \(x = 2\) into \(9x+5\):
\(9\times2+5=18 + 5=23\)
Since \(NL\) is the perpendicular bisector of \(KM\) (by the right - angle mark), \(KL=LM\) (a point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment)

Answer:

\(23\)