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if PQ=21 cm and QR=5cm, then what are the possible lengths for PR so that line PQ, line QR, and line PR can form a triangle? explain your reasoning

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Trimid
PR must be less than 26cm as PQ + QR = 26cm

PR must be more than 16cm as PD- QR = 16cm

At both those limits the sides would lay on top of each other.
Calculistaid

Let

x---------> the possible lengths for PR


we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

so

case 1)

[tex] x+5 >21\\ x >16 [/tex]cm


case 2)

[tex] x+21 > 5\\ x >-16 [/tex]cm


case 3)

[tex] 21+5 > x\\ 26 > x\\ x < 26 [/tex]cm

so

[tex] 16 < x < 26 [/tex]

therefore


the answer is

PR must be less than [tex] 26 [/tex]cm and must be more than [tex] 16 [/tex]cm

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