If R is the midpoint of TS, TR = 5x - 12, and RS = 3x + 8, find TS.

Applying the segment addition theorem, the value of TS is: 76

Given:

TR = 5x - 12

RS = 3x + 8

If T is the midpoint of TS, therefore we would have the following equation:

TR = RS

5x - 12 = 3x + 8

5x - 3x = 12 + 8

2x = 20

x = 10

TS = TR + RS (segment addition theorem)

TS = 5x - 12 + 3x + 8

TS = 5(10) - 12 + 3(10) + 8

TS = 50 - 12 + 30 + 8

TS = 76

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5x -12 = 3x +8 (set the two = each other because they are the same length)

2x- 12= 8 (subtract 3x from both sides)

2x = 20 (add 12 to both sides)

x=10 (what x= for both expressions)

5(10) -12 (plug it into the first one to see what the length is and to see they're =

50 - 12 ( I already multiplied, now subtract)

38 (what the length of TR is)

3(10) +8 (plug it in again but into the other expression)

30+8 (multiply and add)

38 (the two have the same answer, so the x-value is correct.)

38+38= 76 (add the lengths of RS and TR and you get the length of TS)

Step-by-step explanation:

I hope this helps :)

∠cbe and ∠deb are same-side interior angles.

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