Perimeter of a Rectangle: Extended distributive law

Since in a rectangle each pair of opposite sides are equal to each other, let's call each pair of sides X and Y

Now let's set up a formula to calculate the perimeter of the rectangle:

$2x+2y=14$

Let's divide both sides by 2:

$x+y=7$

From this formula, we'll calculate X:

$x=7-y$

We know that the area of the rectangle equals length times width:

$x\times y=12$

We know that X equals 7 minus Y, let's substitute this in the formula:

$(7-y)\times y=12$

$7y-y^2=12$

$y^2-7y+12=0$

$(y-3)\times(y-4)=0$

From this we can claim that:

$y=3,y=4$

Let's go back to the formula we found earlier:

$x=7-y$

Let's substitute y equals 3 and we get:

$x=7-3=4$

Now let's substitute y equals 4 and we get:

$x=7-4=3$

Therefore, the lengths of the rectangle's sides are 4 and 3