Respuesta :
The length of the line segment 'ln' = 20 units
For given 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 : no is equal to 3 : 1 : 2.
⇒ lm : mn : no = 3 : 1 : 2
If the ratio is multiplied by x, which is the factor that brings the ratio to its original value,
lm : mn : no = 3x : 1x : 2x
So, the length of the line segments lm, mn, and no are 3x, 1x, and 2x, respectively.
We have been given the distance lo is 30 units.
⇒ 3x + 1x + 2x = 30
⇒ 6x = 30
⇒ x = 5
We need to find the length of line segment ln.
⇒ ln = lm + mn
⇒ ln = 3x + 1x
⇒ ln = x(3 + 1)
⇒ ln = 4x
⇒ ln = 4(5)
⇒ ln = 20 units
Therefore, the length of the line segment 'ln' = 20 units
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