Question

if ns = 4, find sr.

Explanation:

Step1: Recall the centroid theorem

The centroid of a triangle divides each median into a ratio of \(2:1\). Here, \(S\) is the centroid of \(\triangle NOM\) (since \(NQ = QO\), \(MP\) is a median, \(OR\) is a median). For the median \(MO\), \(NS:SR = 2:1\).

Step2: Set up the proportion

Let \(SR=x\). Given \(NS = 4\), and from the ratio \(NS:SR=2:1\), we have the equation \(\frac{NS}{SR}=\frac{2}{1}\). Substituting \(NS = 4\) into the equation \(\frac{4}{x}=\frac{2}{1}\).

Step3: Solve for \(x\)

Cross - multiply: \(2x=4\times1\). Then \(x = 2\) using the formula \(x=\frac{4\times1}{2}\).

Answer:

\(2\)