As given by the question
There are given that the perimeter of the triangle is 141 meters.
Now,
From the formula of the perimeter of the triangle:
[tex]P=a+a+a[/tex]Where, a are represent three sides of the given triangle
So,
Put the value of sides into the given formula
Then,
[tex]\begin{gathered} P=a+a+a \\ 141=5x+7x+2+7x+6 \\ 141=19x+8 \\ 19x=141-8 \\ 19x=133 \\ x=7 \end{gathered}[/tex]Then, put the value x into all side
So,
The length of side measuring 5x is:
[tex]\begin{gathered} 5x=5\times7 \\ =35 \end{gathered}[/tex]The length of side measuring (7x+2) is;
[tex]\begin{gathered} 7x+2=7(7)+2 \\ =49+2 \\ =51 \end{gathered}[/tex]And,
The length of sides measuring (7x+6) is:
[tex]\begin{gathered} 7x+6=7(7)+6 \\ =49+6 \\ =55 \end{gathered}[/tex]