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

`|LN| = 24`

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| = (LN)/(LN+NO)*|LO|`

`|LN| = (4)/(4+1)*30`

`|LN| = (4)/(5)*30`

`|LN| = (4*30)/(5)`

`|LN| = (120)/(5)`

`|LN| = 24`