SOLUTION: If PQ = 21 cm and QR = 5 cm, then what are the possible lengths for PR so that PQ, QR , and PR can form a triangle? Explain your reasoning.

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Question 394686: If PQ = 21 cm and QR = 5 cm, then what are the possible lengths for PR so that PQ, QR , and PR can form a triangle? Explain your reasoning.
Found 2 solutions by ewatrrr, richard1234:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

third side PR <26cm

Note: the sum of the lengths of two sides of a triangle must be greater than 3rd side

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of any two sides must be longer than the third side. This means,

PQ+%2B+QR+%3E+PR --> 21+%2B+5+%3E+PR --> PR+%3C+26

QR+%2B+PR+%3E+PQ --> 5+%2B+PR+%3E+21 --> PR+%3E+16

The last inequality, PQ+%2B+PR+%3E+QR is already implied as PQ+%3E+QR so this doesn't limit PR.

Putting the inequalities together, we have 16+%3C+PR+%3C+26.