Question

in \\( \triangle h i j \\), \\( n \\) is the centroid. if \\( l j = 19 \\), find \\( i l \\).

Explanation:

Step1: Recall the property of centroid

The centroid of a triangle divides each median into a ratio of \(2:1\). Also, the median of a triangle bisects the side of the triangle. So if \(N\) is the centroid and \(IL\) is a median, then \(IL = LJ+IL\) and \(LJ = IL\) (because the median bisects the side \(HJ\)).

Step2: Calculate \(IL\)

Since \(LJ = 19\) and \(IL\) is a median (so \(IL = LJ + IL\), but actually \(IL\) is composed of two - equal parts where \(LJ\) is one part). By the property of the median (bisects the side), \(IL=2\times LJ\). Substitute \(LJ = 19\) into the formula.

\(IL=2\times19 = 38\)

Answer:

\(38\)