Question

if ( nk = 13 ), find ( jk ).

Explanation:

Step1: Use the property of the centroid

In a triangle, the centroid divides each median into a ratio of \(2:1\). Here, \(N\) is the centroid, \(IK\) is a median (since \(K\) is the mid - point of \(HI\)), and \(NK\) is part of the median \(IK\). Let \(JK\) be \(x\).
We know that \(NK=\frac{1}{3}JK\) (because the centroid divides the median such that the segment from the vertex to the centroid is twice the segment from the centroid to the mid - point of the side, i.e., \(JK = 3NK\)).

Step2: Substitute the value of \(NK\)

Given \(NK = 13\). Substitute \(NK\) into the formula \(JK = 3NK\).
So, \(JK=3\times13\).

Answer:

\(JK = 39\)