Given in the picture,
- ΔJKL, with LO = 104 cm
- Points M, N and P are the midpoints of sides JL, JK and KL respectively.
Since, M, N and P are the midpoints of the given sides, JP, LN and KM will be the medians of the triangle meeting at a common point O.
Therefore, point O will be the centroid of the triangle.
Property of the centroid of a triangle,
- Centroid of a triangle divides the medians in the ratio of 2 : 1.
By this property,
[tex]\frac{LO}{NO}= \frac{2}{1}[/tex]
[tex]\frac{104}{NO}= \frac{2}{1}[/tex]
NO = 52 cm
Therefore, NO = 52 cm will be the answer.
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