Question

LM is a perpendicular bisector of ​NP. The length of ​LN is 12w+7, and the length of ​LP is 15w−5. What is the length of ​LN?

Answer 1

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.

`LN=LP`

`12w+7=15w-5`

Isolate variable terms.

`7+5=15w-12w`

`12=3w`

Divide both sides by 3.

`(12)/(3)=w`

`w=4`

Now,

`LN=12w+7`

`LN=12(4)+7`

`LN=48+7`

`LN=55`

Therefore, the length of ​LN is 55 units.