Why difference between area and perimeter is always 4 if one side of a rectangle is 2?

We can answer this by analyzing the algebraic formulas for perimeter and area of any given rectangle.

Assuming the length of the rectangle is 2 and the width is x we have the following diagram (ignore the periods they are just spacers since Answers.com won't let me format a diagram properly):

... _____x______

...|......................|

2 |......................| 2

...|___________|

............ x

Area is found by multiplying the length times width, so we get: A = 2x

The perimeter is found by adding all the sides, thus: P = x + x + 2 + 2

which simplifies to the following: P = 2x + 4

Here we can see that since A = 2x, and P = 2x + 4, that by using substitution (plugging in A where 2x is in the P formula) we find the formula for perimeter is the Area plus 4:

P = A + 4

So this shows that for any rectangle with a side length of 2 and another of any length x, the perimeter will always be 4 more than the area.