A rectangle has a length of 4x and a width of 4x-2. Its perimeter is 12 inches. Find the length and width. Write the equations. What is the length and width?
To solve this problem, we need to use the information given and set up equations based on it.
Let's start by setting up the equation for the perimeter of a rectangle, which is the sum of all four sides. We are given that the perimeter is 12 inches.
Perimeter of a rectangle = 2(length + width)
Using the given information, the equation becomes:
2(4x + 4x-2) = 12
Simplifying the equation:
2(8x - 2) = 12
Next, we can distribute the 2 to the terms inside the bracket:
16x - 4 = 12
Now, let's isolate the variable by moving the constant term to the other side of the equation:
16x = 12 + 4
16x = 16
Finally, divide both sides of the equation by 16 to solve for x:
x = 16/16
Simplifying further, we find that x = 1.
Now that we know the value of x, we can substitute it back into the expressions for length and width to find their values:
Length = 4x = 4(1) = 4 inches
Width = 4x-2 = 4(1)-2 = 2 inches
Therefore, the length of the rectangle is 4 inches and the width is 2 inches.
2(4x) + 2(4x-2) = 12
8x + 8x - 4 = 16
16x = 16
x = 1
one side is 4, the other is 2