We have a triangle with perimeter P = 65ft and sides:
[tex]\begin{gathered} l_1=n, \\ l_2=3n+5, \\ l_3=3n+4. \end{gathered}[/tex]The perimeter of a geometrical figure is just the sum of the sides. In this case, we have:
[tex]P=l_1+l_2+l_3._{}[/tex]Replacing the data of the problem, we have:
[tex]\begin{gathered} 65=(n)+(3n+5)+(3n+4) \\ 65=7n+9. \end{gathered}[/tex]Solving for n the last equation, we get:
[tex]\begin{gathered} 7n=65-9, \\ 7n=56, \\ n=\frac{56}{7}=8. \end{gathered}[/tex]Replacing the value n = 8 in the equations for each side, we get:
[tex]\begin{gathered} l_1=8, \\ l_2=3\cdot8+5=24+5=29, \\ l_3=3\cdot8+4=24+4=28. \end{gathered}[/tex]Answer
The lengths of the sides are 8ft, 29ft and 28ft.
