The lengths of RT and TW in triangle QUW, with centroid T, are determined to be 4 units and 2 units, respectively, based on the centroid property and the given information about the triangle's medians.
In a triangle, the centroid is the point of concurrency of the medians, dividing each median into two segments with a ratio of 2:1. Given that point T is the centroid of triangle QUW, we can use the centroid property to find the lengths of RT and TW.
Let's denote the length of the median from vertex U to T as MU, from vertex W to T as MW, and from vertex Q to T as MQ. Since T is the centroid, MQ = 2 * TW and MU = 2 * RT.
It's given that RW = 6, and since TW is one-third of RW, TW = 6 / 3 = 2. Using the ratios, we find RT = MU / 2 = RW - TW = 6 - 2 = 4.
Therefore, RT = 4 units and TW = 2 units in triangle QUW with centroid T. The centroid divides the medians in a consistent 2:1 ratio, allowing us to determine the lengths of RT and TW based on the given information.
Complete question:
In △QUW, point T is the centroid, and RW = 6. Find RT and TW.