Question

Solve S=2(lw + lh + wh) for w

Answer 1

Dividing by 2, we have S/2=lw+lh+wh. After that, we subtract lh from both sides to get S/2-lh=lw+wh. Next, we divide both sides by w to get (S/2)/w=l+h. Next, we divide by S/2 to get 1/w=(l+h)/(S/2). Lastly, we multiply by w and divide by (l+h)/(S/2)  to get w=(S/2)/(l+h)

Answer 2

The value of the equation for w is
`w=(S-2lh)/(2l+2h)`.

Explanation:

Consider the provided equation.

`S=2(lw + lh + wh)`

We need to solve the equation for w.

Distributive property:

`a(b+c)=ab+ac`

Use the above property.

`S=2lw + 2lh + 2wh`

Subtract 2lh from both the sides.

`S-2lh=2lw+ 2wh`

Take w common from the right side.

`S-2lh=w(2l+ 2h)`

Divide both the side by 2l+2h.

`(S-2lh)/(2l+2h)=(w(2l+ 2h))/(2l+2h)`

`w=(S-2lh)/(2l+2h)`

Hence, the value of the equation for w is
`w=(S-2lh)/(2l+2h)`.