Question 1063823
For a given triangle PQR, the sum of any two sides is greater than the third and any side is less than the sum of the other two
:
1) PQ + PR > RQ
:
2) PQ + RQ > PR 
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3) RQ + PR > PQ
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4) RQ < 11
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5) PR = RQ + 4
:
by inequality 2) and equation 5)
:
PQ + RQ > RQ + 4
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6) PQ > 4
:
any side of PQR is less than the sum of the other two sides, also use inequality 4)
:
RQ < PQ + PR < 11
:
use equation 5)
:
RQ < PQ + RQ + 4 < 11
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7) 0 < PQ < 7
:
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combine inequalities 6) and 7)
:
4 < PQ < 7
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