Question

in △hij, n is the centroid. if lj = 19, find il. answer attempt 1 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.

Step2: Use the mid - point property

Since \(N\) is the centroid and \(IL\) is a median (because \(N\) is the centroid and \(L\) lies on \(HJ\)), and \(L\) is the mid - point of \(HJ\). By the definition of a mid - point, if \(LJ = 19\), then \(IL=IJ\) (because \(L\) is the mid - point of \(HJ\) and \(IL\) is a median), and \(IL = 2\times LJ\).

Step3: Calculate the value of \(IL\)

Substitute \(LJ = 19\) into the formula \(IL = 2\times LJ\). So, \(IL=2\times19 = 38\).

Answer:

\(38\)