Question

in △opq, u is the intersection of the three medians. if ou = 16, find us.

Explanation:

Step1: Recall the property of the centroid of a triangle

The centroid \(U\) of a triangle divides each median into a ratio of \(2:1\). That is, if a median is \(OU + US\), then \(OU:US = 2:1\).

Step2: Set up the equation based on the ratio

Let \(US=x\). Since \(OU = 16\) and \(OU:US=2:1\), we have the equation \(\frac{OU}{US}=\frac{2}{1}\). Substituting \(OU = 16\) into the equation, we get \(\frac{16}{x}=\frac{2}{1}\).

Step3: Solve the equation for \(x\)

Cross - multiply the equation \(16\times1=2\times x\). Then \(2x = 16\), and dividing both sides by \(2\) gives \(x=\frac{16}{2}=8\). So \(US = 8\).

Answer:

\(8\)