The length of a rectangular piece of steel in a bridge is 4
meters less than triple
the width. The perimeter of the piece of steel is 56
meters. Find the length of the piece of steel. Find the width of the piece of steel.
width ---- x
length ----3x-4
perimeter = 2widths + 2 lengths
56 = 2x + 2(3x-4)
carry on
Let's solve this step-by-step:
Let's denote the length of the piece of steel as L and the width as W.
Step 1: Translate the given information into equations:
According to the problem, the length of the piece of steel is 4 meters less than triple the width, so we can write the equation:
L = 3W - 4
The perimeter of a rectangle is given by the formula:
Perimeter = 2L + 2W = 56
Step 2: Substitute the value of L from the first equation into the second equation:
2(3W - 4) + 2W = 56
Simplify the equation:
6W - 8 + 2W = 56
8W - 8 = 56
Step 3: Solve the equation for W:
8W - 8 = 56
8W = 56 + 8
8W = 64
W = 64/8
W = 8
Step 4: Substitute the value of W back into the first equation to find L:
L = 3W - 4
L = 3(8) - 4
L = 24 - 4
L = 20
Therefore, the length of the piece of steel is 20 meters and the width is 8 meters.
To find the length and width of the rectangular piece of steel, we will set up a system of equations based on the given information.
Let's assume the width of the piece of steel is represented by "w" (in meters).
According to the problem, the length of the piece of steel is 4 meters less than triple the width. So, the length can be represented as "3w - 4" (in meters).
The perimeter of a rectangle is calculated by adding the lengths of all its sides. In this case, the perimeter is given as 56 meters.
The formula for the perimeter of a rectangle is:
Perimeter = 2 * (length + width)
Substituting the values:
56 = 2 * ((3w - 4) + w)
Now, we can solve this equation to find the value of "w" (width):
56 = 2 * (4w - 4)
56 = 8w - 8
8w = 56 + 8
8w = 64
w = 64 / 8
w = 8
Now, we can substitute the value of "w" back into the expression for the length:
Length = 3w - 4 = 3 * 8 - 4 = 24 - 4 = 20
Therefore, the length of the piece of steel is 20 meters, and the width is 8 meters.