Question

in △fgh, l is the centroid. if hl = 12, find li.

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median into a ratio of \(2:1\), with the longer segment being closer to the vertex.

Step2: Apply to \(HL\) and \(LI\)

In \(\triangle FGH\), \(H\) to \(L\) to \(I\) is part of a median (since \(L\) is centroid). So \(HL:LI = 2:1\). Let \(LI = x\), then \(HL = 2x\).

Step3: Solve for \(x\)

Given \(HL = 12\), so \(2x = 12\). Divide both sides by 2: \(x=\frac{12}{2}=6\). Thus, \(LI = 6\).

Answer:

6