Question

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

Answer 1

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.

Answer 2

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)

$x+5 >21\\ x >16$cm

case 2)

$x+21 > 5\\ x >-16$cm

case 3)

$21+5 > x\\ 26 > x\\ x < 26$cm

so

$16 < x < 26$

therefore

the answer is

PR must be less than $26$cm and must be more than $16$cm