Question

in △hij, n is the centroid. if lj = 19, find il. answer attempt 2 out of 2 il =

Explanation:

Step1: Recall the property of the centroid

The centroid of a triangle divides each median into a ratio of \(2:1\). Also, a median of a triangle connects a vertex to the mid - point of the opposite side. So, if \(N\) is the centroid of \(\triangle HIJ\) and \(IL\) is a median, then \(L\) is the mid - point of \(HJ\).

Step2: Use the mid - point property

Since \(L\) is the mid - point of \(HJ\), we have \(IL = LJ+IL\) and \(IL = 2LJ\) (because \(IL\) is composed of two equal segments \(IL = IL_1+IL_2\) where \(IL_1 = LJ\) and \(IL_2 = LJ\) as \(L\) is the mid - point). Given \(LJ = 19\), then \(IL=IL_1 + IL_2\) and \(IL_1=IL_2 = LJ\).

Answer:

\(IL = 38\)