Question

in $\triangle jkl$, $q$ is the centroid and $ml = 48$.
$mq=square$$ql=square$

Explanation:

Step1: Recall the property of the centroid

The centroid divides each median into a ratio of \(2:1\). Also, \(ML\) is a median and \(M\) is the mid - point of \(JK\). So \(JM = MK\). And \(MQ:QL=1:2\) and \(ML = MQ + QL\). Let \(MQ=x\), then \(QL = 2x\).

Step2: Substitute into the equation for \(ML\)

Since \(ML=48\), and \(ML=MQ + QL\), we have \(x + 2x=48\). Combining like terms gives \(3x=48\). Solving for \(x\) by dividing both sides by \(3\), we get \(x=\frac{48}{3}=16\).
So \(MQ = 16\).

Step3: Find \(QL\)

Since \(QL = 2x\) and \(x = 16\), then \(QL=2\times16 = 32\).

Answer:

\(MQ = 16\), \(QL = 32\)