Answers:
RS = 13
ST = 8
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Explanation:
S is between R and T. I'm assuming also that S is on line RT.
If that's the case, then by the segment addition postulate, we can say RS+ST = RT.
In other words, the longest segment RT is broken into two smaller pieces RS and ST (not necessarily equal but they may be). Gluing the pieces back together should get us the original longest segment.
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Apply substitution and solve for x.
RS+ST = RT
(2x+5)+(3x-4) = 21
(2x+3x)+(5-4) = 21
5x+1 = 21
5x = 21-1
5x = 20
x = 20/5
x = 4
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If x = 4, then,
- RS = 2x+5 = 2*4+5 = 13
- ST = 3x-4 = 3*4-4 = 8
Then notice how RS+ST = 13+8 = 21, which is is the length of RT
This confirms that RS+ST = RT is true and it confirms our answers.
