Question

Literal equation S=2 (lw+lh+wh) solve for w

Answer 1

$S=2\left( lw+lh+wh \right) \\ \\ S=2\left\{ w\left( l+h \right) +lh \right\} \\ \\ \frac { 1 }{ 2 } \cdot S=2\left\{ w\left( l+h \right) +lh \right\} \cdot \frac { 1 }{ 2 } \\ \\ \frac { S }{ 2 } =w\left( l+h \right) +lh\\ \\ w\left( l+h \right) =\frac { S }{ 2 } -lh\\ \\ \frac { 1 }{ \left( l+h \right) } \cdot w\cdot \left( l+h \right) =\frac { 1 }{ \left( l+h \right) } \left( \frac { S }{ 2 } -lh \right)$

$\\ \\ w=\frac { 1 }{ \left( l+h \right) } \left( \frac { S }{ 2 } -lh \right)$