A piece of metal is bent into a rectangle and has a length which is 5 times as long as its width. If the perimeter of the piece of metal is 13 feet 6 inches, find the length and the width of the piece of sheet metal.
You must use a variable , write an equation and solve the equation!
5(X) = 13' 6"
5(X) = 162 inches
32.4 inches or 2.7 feet
is this correct
no
if the width is x feet then the length is 5x feet
perimeter = 2width + 2 length
so ..
2x + 2(5x) = 13.5
12x = 13.5
x = 1.125 feet
so the width is 1 1/8 feet
the length is 5(1.125) = 5 5/8 feet
i like to do maths
Yes, your calculation is correct. Let me explain the process step by step:
Let's denote the width of the metal piece as 'x'.
According to the problem, the length of the metal piece is 5 times its width, which means the length would be 5x.
To find the perimeter of the metal piece, we add up the lengths of all four sides. Since it is a rectangle, opposite sides have the same length. Therefore, the perimeter can be calculated as follows:
Perimeter = 2(length) + 2(width)
Perimeter = 2(5x) + 2(x)
Perimeter = 10x + 2x
Perimeter = 12x
We are given that the perimeter of the metal piece is 13 feet 6 inches, which can be converted to inches as you did:
13 feet 6 inches = 13 * 12 inches + 6 inches = 156 inches + 6 inches = 162 inches
Now we can set up the equation:
12x = 162
To solve for x, divide both sides of the equation by 12:
x = 162 / 12
x = 13.5
Therefore, the width of the metal piece is 13.5 inches.
To find the length, we can substitute the value of x in the equation for the length:
Length = 5x
Length = 5 * 13.5 = 67.5 inches
Finally, you converted inches to feet correctly as well:
67.5 inches = 67.5 / 12 feet = 5.625 feet = 5 feet 7.5 inches
So, the length of the metal piece is 5 feet 7.5 inches (or 67.5 inches) and the width is 13.5 inches (or 1.125 feet).