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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.

Respuesta :

MrRoyal

Answer:

[tex]|LN| = 24[/tex]

Step-by-step explanation:

Given

[tex]LM:MN:NO = 3:1:2[/tex]

[tex]LO = 30[/tex]

Required

Find LN

[tex]LN = LM + MN[/tex]

From the ratio, LM = 3 and MN = 1

So:

[tex]LN = 3 + 1[/tex]

[tex]LN = 4[/tex]

LN and NO can be represented as:

[tex]LN : NO = 4 : 1[/tex]

The length of LN is then calculated as:

[tex]|LN| = \frac{LN}{LN+NO}*|LO|[/tex]

[tex]|LN| = \frac{4}{4+1}*30[/tex]

[tex]|LN| = \frac{4}{5}*30[/tex]

[tex]|LN| = \frac{4*30}{5}[/tex]

[tex]|LN| = \frac{120}{5}[/tex]

[tex]|LN| = 24[/tex]