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If TU = x + 8, UV = 5x + 20, and TV 14x + 20, what is TV?

User Hanksims
by
2.7k points

1 Answer

12 votes
12 votes

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.

User Davidmontoyago
by
3.2k points
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