Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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

Sagot :

Trim
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.
calculista

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

Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.