In this problem, we have a triangle with sides:
• PR = 4x,,
,
• RQ = x + 3,
,
• QP = 5x - 1,
,
• and perimeter p = 72.
By definition, the perimeter is the sum of the length of the sides, so we have:
[tex]\begin{gathered} p=PR+RQ+QP, \\ 72=(4x)+(x+3)+(5x-1)\text{.} \end{gathered}[/tex]
Solving for x the last equation, we find that:
[tex]\begin{gathered} 72=10x+2, \\ 72-2=10x \\ 70=10x \\ x=\frac{70}{10}=7. \end{gathered}[/tex]
Replacing the value x = 7 in the equation of side PR, we have:
[tex]PR=4\cdot7=28.[/tex]
Answer
PR = 28
