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 52 meters. Find the length of the piece of steel. Find the width of the piece of steel
Let "L"= length
Let "W"= width
2L+2W= 52
3W-2= L
substitute in for "L"
2(3W-2)+2W=52
distribute/add
8W-4=52
isolate variable
56=8W
divide
w=7
2L+14=52
2L=38
L=19
Let's denote the width of the piece of steel as "w" meters.
According to the given information, the length is 2 meters less than triple the width, so its length can be expressed as 3w - 2.
The perimeter of a rectangle is obtained by adding all four sides. In this case, the perimeter is given as 52 meters.
Using the formula for the perimeter of a rectangle:
Perimeter = 2 * (length + width)
Substituting the given values, we can write the equation as:
52 = 2 * (3w - 2 + w)
Simplifying the equation:
52 = 2 * (4w - 2)
52 = 8w - 4
56 = 8w
w = 7
Therefore, the width of the piece of steel is 7 meters.
To find the length:
Length = 3w - 2
Length = 3 * 7 - 2
Length = 21 - 2
Length = 19
So, the length of the piece of steel is 19 meters.
To find the length and width of the rectangular piece of steel, we need to use the given information about the relationship between the length and width, as well as the perimeter of the steel.
Let's assume the width of the piece of steel is 'w' meters.
According to the given information, the length is 2 meters less than triple the width.
So, the length can be represented as 3w - 2 meters.
The perimeter of a rectangle is calculated by adding the lengths of all its sides. In this case, the perimeter is given as 52 meters, so we can set up an equation using the length and width:
Perimeter = 2(Length + Width)
52 = 2((3w - 2) + w)
Simplifying the equation:
52 = 2(4w - 2)
52 = 8w - 4
52 + 4 = 8w
56 = 8w
w = 7
Now that we have the value of the width, we can substitute it into the expression for the length:
Length = 3w - 2
Length = 3(7) - 2
Length = 21 - 2
Length = 19
Therefore, the length of the piece of steel is 19 meters and the width is 7 meters.