Let "x" represent the width of the rectangular steel, then the length, which is 2meters less than triple the width, can be expressed as "3x-2".
The perimeter of the rectangular piece is 60meters.
The formula for the perimeter is the following:
[tex]P=2w+2l[/tex]Replace the formula with the expressions for the width and length and the given perimeter of the piece of steel:
w=x
l=3x-2
P=60
[tex]60=2x+2(3x-2)[/tex]From this expression, you can determine the value of x.
-First, distribute the multiplication on the parentheses term
[tex]\begin{gathered} 60=2x+2\cdot3x-2\cdot2 \\ 60=2x+6x-4 \end{gathered}[/tex]-Second, simplify the like terms and pass "-4" to the left side of the expression by applying the opposite operation "+4" to both sides of it
[tex]\begin{gathered} 60=8x-4 \\ 60+4=8x-4+4 \\ 64=8x \end{gathered}[/tex]-Third, divide both sides by 8 to determine the value of x
[tex]\begin{gathered} \frac{64}{8}=\frac{8x}{8} \\ 8=x \end{gathered}[/tex]The value of x is 8m, which means that the width of the piece of steel is 8m
To determine the length you just have to replace the expression by x=8
[tex]\begin{gathered} l=3x-2 \\ l=3\cdot8-2 \\ l=24-2 \\ l=22 \end{gathered}[/tex]The length is 22m
