Final answer:
To solve for x, we use the property of medians dividing a segment into two equal parts and set up the equation 2(x + 3) = (4x - 18), leading to the solution x = 12.
Step-by-step explanation:
The subject of the question is about finding the value of x in a geometry problem involving medians in a triangle. In triangle ABC, BD and CE are medians, with given expressions for lengths BG and BD that involve x. To find the value of x, we need to use the fact that the median of a triangle divides it into two segments of equal length.
Since BD is a median, it will divide BG into two equal parts, which means BG is half the length of BD. Therefore, we can set up the equation: 2(BG) = BD. Substituting the given expressions, we get 2(x + 3) = (4x - 18). When we solve for x, we find:
- 2(x + 3) = 4x - 18
- 2x + 6 = 4x - 18
- 6 + 18 = 4x - 2x
- 24 = 2x
- x = 12