Solve for L

Question

The surface area of a rectangular solid of a length L, width W, and height H is given by the formula:

S=2LH+2LW=2WH

Answer 1

S=2LH+2LW+2WH

S-2WH=2LH+2LW

S-2WH=L(2H+2W)

(S-2WH)/(2H+2W)=L

Answer 2

So the approach here is that we NEED to isolate all values that contain L on ONE side of the equation

 

2LH + 2LW = 2WH

You can factor 2L out of the left side to get:

2L(H + W) = 2WH

 

Divide BOTH sides by 2(H+W)

 

2L(H+W)        2WH

----------- = ----------

 2(H+W)       2(H+W)

 

We can then CANCEL OUT the 2 and the (H+W) on the LEFT SIDE

         2WH

L = ----------

      2(H+W)

 

Now we can CANCEL OUT the 2 on the right side ...

         WH

L = ---------

       H + W

 

This is your ANSWER :) 

on one line

L = (WH)/(H+W)