Question

if ( dh = 30 ), find ( jh ).

Explanation:

Step1: Recall the centroid theorem

The centroid of a triangle divides each median into a ratio of \(2:1\). That is, if \(D\) is a vertex and \(H\) is the mid - point of a side (so \(EH\) is a median), and \(J\) is the centroid, then \(DJ:JH = 2:1\) and \(DH=DJ + JH\). Let \(JH=x\), then \(DJ = 2x\).

Step2: Substitute into the \(DH\) equation

Since \(DH = 30\) and \(DH=DJ+JH\), and \(DJ = 2x\), \(JH=x\), we have \(30=2x + x\).

Step3: Solve for \(x\)

Combine like terms: \(30 = 3x\). Then, divide both sides by \(3\): \(x=\frac{30}{3}=10\).

Answer:

\(10\)