Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.