Question

The points L, M, N and O all lie on the same line segment, in that order, such that the ratio of LM:MN:NOLM:MN:NO is equal to 3:1:2.3:1:2. If LO=30,LO=30, find LN.LN.

Answer 1

Answer:

$|LN| = 24$

Step-by-step explanation:

Given

$LM:MN:NO = 3:1:2$

$LO = 30$

Required

Find LN

$LN = LM + MN$

From the ratio, LM = 3 and MN = 1

So:

$LN = 3 + 1$

$LN = 4$

LN and NO can be represented as:

$LN : NO = 4 : 1$

The length of LN is then calculated as:

$|LN| = \frac{LN}{LN+NO}*|LO|$

$|LN| = \frac{4}{4+1}*30$

$|LN| = \frac{4}{5}*30$

$|LN| = \frac{4*30}{5}$

$|LN| = \frac{120}{5}$

$|LN| = 24$