The perimeter P of a rectangle is given by the formula P = 2L + 2W where El is the length and W is the width. Solve the formula for L

Question

The perimeter P of a rectangle is given by the formula P = 2L + 2W where El is the length and W is the width. Solve the formula for L

 

please leave in depth explanations for each step.  

Answer 1

Solving the formula for L means getting the L by itself on one side of the equation with everything else on the other side.  Here's how it's done:

 

P = 2L + 2W

 

First, let's move the 2W to the other side by subtracting 2W from both sides of the equation.  What ever operation we do to one side we also have to do to the other side to keep things equal:

 

      P - 2W = 2L + 2W - 2W

 

Since 2W - 2W = 0, it reduces to:

 

      P - 2W = 2L

 

Now we just need to get rid of the factor of 2 that multiplies the L.  We undo multiplication with division, so divide both sides by 2:

 

     (P-2W)/2 = 2L/2

 

Since 2L/2 = L, we have:

 

      (P-2W)/2 = L

 

and we're done!