Final answer:
To find KG, we can set up an equation using the fact that L is the centroid of EFG. The formula for finding the ratio of the longer segment to the shorter segment of a median can help us solve for KG.
Step-by-step explanation:
To find KG, we need to first determine the value of x. We can start by setting up an equation using the fact that L is the centroid of EFG. The centroid divides each median into two segments, with the ratio of the longer segment to the shorter segment equal to 2:1.
So, we have:
(KG)/(EK) = 2/1
Substituting the given values, we get:
(KG)/(3x + 13) = 2/1
Cross multiplying and solving for KG, we have:
KG = (2(3x + 13))/1 = 6x + 26