Question

The length of a rectangular piece of steel in a bridge is 2 meters less than triple the width. The perimeter of the piece of steel is 60 meters. Find the length of the pieceof steel. Find the width of the piece of steel.

Answer 1

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:

`P=2w+2l`

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

`60=2x+2(3x-2)`

From this expression, you can determine the value of x.

-First, distribute the multiplication on the parentheses term

`\begin{gathered} 60=2x+2\cdot3x-2\cdot2 \\ 60=2x+6x-4 \end{gathered}`

-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

`\begin{gathered} 60=8x-4 \\ 60+4=8x-4+4 \\ 64=8x \end{gathered}`

-Third, divide both sides by 8 to determine the value of x

`\begin{gathered} (64)/(8)=(8x)/(8) \\ 8=x \end{gathered}`

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

`\begin{gathered} l=3x-2 \\ l=3\cdot8-2 \\ l=24-2 \\ l=22 \end{gathered}`

The length is 22m