Solve for H s=2LW+2LH+2WH

$s = 2 L W + 2 L H + 2 W H$

Step 1

Rewrite the equation as $2 L W + 2 L H + 2 W H = s$ .

$2 L W + 2 L H + 2 W H = s$

Step 2

Subtract $2 L W$ from both sides of the equation.

$2 L H + 2 W H = s - 2 L W$

Step 3

Factor $2 H$ out of $2 L H + 2 W H$ .

Factor $2 H$ out of $2 L H$ .

$2 H (L) + 2 W H = s - 2 L W$

Factor $2 H$ out of $2 W H$ .

$2 H (L) + 2 H (W) = s - 2 L W$

Factor $2 H$ out of $2 H (L) + 2 H (W)$ .

$2 H (L + W) = s - 2 L W$

Step 4

Divide each term in $2 H (L + W) = s - 2 L W$ by $2 (L + W)$ and simplify.

Divide each term in $2 H (L + W) = s - 2 L W$ by $2 (L + W)$ .

$\frac{2 H (L + W)}{2 (L + W)} = \frac{s}{2 (L + W)} + \frac{- 2 L W}{2 (L + W)}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 H (L + W)}{2 (L + W)} = \frac{s}{2 (L + W)} + \frac{- 2 L W}{2 (L + W)}$

Rewrite the expression.

$\frac{H (L + W)}{L + W} = \frac{s}{2 (L + W)} + \frac{- 2 L W}{2 (L + W)}$

Cancel the common factor of $L + W$ .

Cancel the common factor.

$\frac{H (L + W)}{L + W} = \frac{s}{2 (L + W)} + \frac{- 2 L W}{2 (L + W)}$

Divide $H$ by $1$ .

$H = \frac{s}{2 (L + W)} + \frac{- 2 L W}{2 (L + W)}$

Simplify the right side.

Simplify each term.

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

Factor $2$ out of $- 2 L W$ .

$H = \frac{s}{2 (L + W)} + \frac{2 (- L W)}{2 (L + W)}$

Cancel the common factors.

Cancel the common factor.

$H = \frac{s}{2 (L + W)} + \frac{2 (- L W)}{2 (L + W)}$

Rewrite the expression.

$H = \frac{s}{2 (L + W)} + \frac{- L W}{L + W}$

Move the negative in front of the fraction.

$H = \frac{s}{2 (L + W)} - \frac{L W}{L + W}$

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

$H = \frac{s}{2 (L + W)} - \frac{L W}{L + W} \cdot \frac{2}{2}$

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

Multiply $\frac{L W}{L + W}$ by $\frac{2}{2}$ .

$H = \frac{s}{2 (L + W)} - \frac{L W \cdot 2}{(L + W) \cdot 2}$

Reorder the factors of $(L + W) \cdot 2$ .

$H = \frac{s}{2 (L + W)} - \frac{L W \cdot 2}{2 (L + W)}$

Combine the numerators over the common denominator.

$H = \frac{s - L W \cdot 2}{2 (L + W)}$

Multiply $2$ by $- 1$ .

$H = \frac{s - 2 L W}{2 (L + W)}$

Solve for H s=2LW+2LH+2WH

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