Given:
LM is a perpendicular bisector of NP.
The length of LN is 12w+7, and the length of LP is 15w−5.
To find:
The length of LN.
Solution:
All points on a perpendicular bisector of a segment are equidistant from the end points of the segment.
Since, LM is a perpendicular bisector of NP, therefore L is equidistant from N and P.
[tex]LN=LP[/tex]
[tex]12w+7=15w-5[/tex]
Isolate variable terms.
[tex]7+5=15w-12w[/tex]
[tex]12=3w[/tex]
Divide both sides by 3.
[tex]\dfrac{12}{3}=w[/tex]
[tex]w=4[/tex]
Now,
[tex]LN=12w+7[/tex]
[tex]LN=12(4)+7[/tex]
[tex]LN=48+7[/tex]
[tex]LN=55[/tex]
Therefore, the length of LN is 55 units.
