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

`LN = 55`

Explanation:

Given

`LN = 12w + 7`

`LP = 15w - 5`

Required

Determine LN

Since LM is a bisector, then we have:

`LP = LN` (See attachment for illustration)

`15w - 5 = 12w + 7`

Collect Like Terms

`15w - 12w = 5 +7`

`3w = 12`

Solve for w

`w = 12/3`

`w = 4`

LN is calculated as thus:

`LN = 12w + 7`

Substitute 4 for w

`LN = 12 * 4 + 7`

`LN = 48 + 7`

`LN = 55`