Answer: 34
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Step-by-step explanation:
I'll assume that all three points are collinear. In the other words, the assumption is that all points are on the same straight line.
The smaller pieces (TU and UV) add to the largest segment TV
We'll use that fact to set up an equation to solve for x.
TU + UV = TV
(x+8) + (5x+20) = 14x+20
6x+28 = 14x+20
6x-14x = 20-28
-8x = -8
x = -8/(-8)
x = 1
Then we can find each segment length based on this x value.
- TU = x+8 = 1+8 = 9
- UV = 5x+20 = 5*1+20 = 25
- TV = 14x+20 = 14*1+20 = 34
Then as a check, we see that TU+UV = 9+25 = 34 = TV which confirms we did things correctly.