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

Answer:

$LN = 55$

Step-by-step 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

$LN = 12 * 4 + 7$

$LN = 48 + 7$

$LN = 55$