A rectangle has a length of 4x and a width of 4x-2. its perimeter is 12 inches find the length and width
P = 2L + 2W
12 = 2(4x) + 2(4x - 2)
12 = 8x + 8x - 4
16 = 16x
1 = x
To find the length and width of the rectangle, we need to set up an equation using the perimeter.
Perimeter of a rectangle = 2(length + width)
Given that the perimeter is 12 inches and the length is 4x while the width is 4x-2, we can substitute the values into the equation:
2(4x + 4x - 2) = 12
Simplifying the equation:
2(8x - 2) = 12
16x - 4 = 12
16x = 16
x = 1
Substituting the value of x back into the original expressions for length and width:
Length = 4x = 4(1) = 4 inches
Width = 4x - 2 = 4(1) - 2 = 4 - 2 = 2 inches
Therefore, the length of the rectangle is 4 inches and the width is 2 inches.
To find the length and width of a rectangle, we need to use the information given about its perimeter.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 12 inches.
Let's label the length of the rectangle as L and the width as W.
From the given information:
Perimeter = 2L + 2W
Substituting the given values:
12 = 2L + 2W
Simplifying the equation:
6 = L + W
Since we are given that the length is 4x and the width is 4x-2, we can substitute these expressions into the equation:
6 = 4x + 4x-2
Combining like terms:
6 = 8x - 2
Adding 2 to both sides:
8 = 8x
Dividing by 8:
x = 1
Now that we have found the value of x, we can substitute it back into the formulas for L and W:
Length = 4x = 4 * 1 = 4 inches
Width = 4x - 2 = 4 * 1 - 2 = 4 - 2 = 2 inches
Therefore, the length of the rectangle is 4 inches and the width is 2 inches.