Question

S=2(lw lh wh) solve for w

Answer 1

You said                                   S = 2(lw + lh + wh)

Divide each side by  2 :            S/2        =  lw + lh + wh

Subtract  'lh'  from each side:   S/2 - lh  =  lw + wh

Factor the right side:                S/2 - lh  =  w(l + h)

Divide each side by  (l + h) :    w  =  (S/2 - lh) / (l + h)

Answer 2

We can't find l exactly since we don't know the values of w, h, and S, but we can simplify this expression.

Simplifying, we have:

S=2(l^2)(w^2)(h^2)

Dividing by 2(w^2)(h^2), we have:

$\frac{S}{2w^2h^2}=l^2$

Taking the square root and rationalizing the denominator, we see that:

$l= \frac{ \sqrt{2S} }{2wh}$