Solve for h a=2lw+2lh+2wh

$a = 2 l w + 2 l h + 2 w h$

Step 1

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

$2 l w + 2 l h + 2 w h = a$

Step 2

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

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

Step 3

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

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

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

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

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

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

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

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $l + w$ .

Cancel the common factor.

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

Divide $h$ by $1$ .

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

Simplify the right side.

Simplify each term.

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

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

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

Cancel the common factors.

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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

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

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 $\frac{2}{2}$ .

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

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

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

Combine the numerators over the common denominator.

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

Multiply $2$ by $- 1$ .

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

Solve for h a=2lw+2lh+2wh

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