Question

what is the length of segment lm?
units

Explanation:

Step1: Set up the equation

Since \(NK = NM\) (marked with equal - length symbols), and \(NL\) is the perpendicular bisector of \(KM\), we have \(NK=NM\). Also, \(KL = LM\) (by the property of the perpendicular bisector of a segment in a triangle). So, \(14x - 3=25\) (because \(NK = NM\)).

$$14x-3 = 25$$

Step2: Solve for \(x\)

Add \(3\) to both sides of the equation:

$$14x=25 + 3$$

$$14x=28$$

Divide both sides by \(14\):

$$x=\frac{28}{14}=2$$

Step3: Find the length of \(KL\)

Substitute \(x = 2\) into the expression for \(KL\): \(KL=9x + 5\)

$$KL=9\times2+5=18 + 5=23$$

Since \(KL = LM\) (by the property of the perpendicular bisector of a segment in a triangle)

Answer:

\(23\)