Final answer:
To determine the length of segment GH, we solve the equation (x + 6) + (x + 5) = 3x + 8 to find x = 3. We then substitute this value back into GH = x + 6 and find that its numerical length is 9 units.
Step-by-step explanation:
To find the numerical length of segment GH, given the lengths GH = x + 6, HI = x + 5, and GI = 3x + 8, we can set up an equation because the segments GH and HI add up to the total length of GI. This concept is based on line segments in geometry.
Therefore, we have the equation:
- GH + HI = GI
- (x + 6) + (x + 5) = 3x + 8
- 2x + 11 = 3x + 8
- 2x - 3x + 11 = 8
- -x = -3
- x = 3
Once we have found x, we can substitute it back to get the length of GH:
- GH = x + 6
- GH = 3 + 6
- GH = 9
Thus, the numerical length of segment GH is 9 units.