The perimeter of a rectangle is given by the sum of the lengths of its four sides.
P = l+r+u+c
but in a rectangle we have essentially two dimensions, the height, and the length, since the upper and bottom sides have the same length and the left and right sides have the same length, then we can also express the perimeter of a rectangle, like this:
l=r=h , left and right side have the same length, we can call it the height of the rectangle
u=c=b, upper and bottom sides have the same length, we can call it the base of the rectangle
P = h+h+b+b = 2h +2b
In this case, we are given the formula P = 6x, and we know that one of the sides has a length of x, as mentioned, opposite sides have the same length, then we will have two sides whose length equals x, then we can express the perimeter like this:
P = 2x + 2y
Where y is the length of the other pair of sites, replacing the equation P = 6x, we get:
6x = 2x + 2y
6x-2x=2y
4x/2=y
y=2x
Then we know that the length of the sides of the rectangles are:
And then the perimeter of the rectangle expressed as the sum of the four sides lengths is:
P = x + x + 2x + 2x