Question

In triangle ARP, centroid E is on median AX. AE is (y/6), and EX is (3y - 2). Find AX.

Answer 1

To find the length of the median AX in triangle ARP, we can use the properties of a centroid.

Step-by-step explanation:

To find the length of the median AX in triangle ARP, we can use the properties of a centroid. The centroid divides the median into two segments, and the length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint of the opposite side. In this case, AE is half the length of AX, so AE = AX/2.

Given that AE = y/6, we can set up the equation y/6 = AX/2 and solve for AX. Cross-multiplying, we get 2(y/6) = AX. Simplifying, we have AX = y/3.