Solve for l s=2lw+2lh+2wh

$s = 2 l w + 2 l h + 2 w h$

Rewrite the equation as $2 l w + 2 l h + 2 w h = s$ .

$2 l w + 2 l h + 2 w h = s$

Subtract $2 w h$ from both sides of the equation.

$2 l w + 2 l h = s - 2 w h$

Factor $2 l$ out of $2 l w + 2 l h$ .

Factor $2 l$ out of $2 l w$ .

$2 l (w) + 2 l h = s - 2 w h$

Factor $2 l$ out of $2 l h$ .

$2 l (w) + 2 l (h) = s - 2 w h$

Factor $2 l$ out of $2 l (w) + 2 l (h)$ .

$2 l (w + h) = s - 2 w h$

Divide each term in $2 l (w + h) = s - 2 w h$ by $2 (w + h)$ and simplify.

Divide each term in $2 l (w + h) = s - 2 w h$ by $2 (w + h)$ .

$\frac{2 l (w + h)}{2 (w + h)} = \frac{s}{2 (w + h)} + \frac{- 2 w h}{2 (w + h)}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 l (w + h)}{2 (w + h)} = \frac{s}{2 (w + h)} + \frac{- 2 w h}{2 (w + h)}$

Rewrite the expression.

$\frac{l (w + h)}{w + h} = \frac{s}{2 (w + h)} + \frac{- 2 w h}{2 (w + h)}$

Cancel the common factor of $w + h$ .

Cancel the common factor.

$\frac{l (w + h)}{w + h} = \frac{s}{2 (w + h)} + \frac{- 2 w h}{2 (w + h)}$

Divide $l$ by $1$ .

$l = \frac{s}{2 (w + h)} + \frac{- 2 w h}{2 (w + h)}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 2$ and $2$ .

Factor $2$ out of $- 2 w h$ .

$l = \frac{s}{2 (w + h)} + \frac{2 (- w h)}{2 (w + h)}$

Cancel the common factors.

Cancel the common factor.

$l = \frac{s}{2 (w + h)} + \frac{2 (- w h)}{2 (w + h)}$

Rewrite the expression.

$l = \frac{s}{2 (w + h)} + \frac{- w h}{w + h}$

Move the negative in front of the fraction.

$l = \frac{s}{2 (w + h)} - \frac{w h}{w + h}$

To write $- \frac{w h}{w + h}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$l = \frac{s}{2 (w + h)} - \frac{w h}{w + h} \cdot \frac{2}{2}$

Write each expression with a common denominator of $2 (w + h)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{w h}{w + h}$ by $\frac{2}{2}$ .

$l = \frac{s}{2 (w + h)} - \frac{w h \cdot 2}{(w + h) \cdot 2}$

Reorder the factors of $(w + h) \cdot 2$ .

$l = \frac{s}{2 (w + h)} - \frac{w h \cdot 2}{2 (w + h)}$

Combine the numerators over the common denominator.

$l = \frac{s - w h \cdot 2}{2 (w + h)}$

Multiply $2$ by $- 1$ .

$l = \frac{s - 2 w h}{2 (w + h)}$

Solve for l s=2lw+2lh+2wh

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