Question

The formula for the surface area of a rectangular prism is `S= 2/w+2wh + 2lh` . How do you solve for `w`?

Answer 1

This is the incorrect formula for the surface area of a rectangular prism. The correct formula is:

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

See below for a process to solve this formula for `w`

Explanation:

First, divide each side of the equation by `color(red)(2)` to eliminate the #parenthesis while keeping the equation balanced:

`S/color(red)(2) = (2(wl + wh + lh))/color(red)(2)`

`S/2 = (color(red)(cancel(color(black)(2)))(wl + wh + lh))/cancel(color(red)(2))`

`S/2 = wl + wh + lh`

Next, subtract `color(red)(lh)` from each side of the equation to isolate the `w` terms while keeping the equation balanced:

`S/2 - color(red)(lh) = wl + wh + lh - color(red)(lh)`

`S/2 - lh = wl + wh + 0`

`S/2 - lh = wl + wh`

Then, factor a `w` from each term on the right side of the equation giving:

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

Now, divide each side of the equation by `color(red)((l + h))` to solve for `w` while keeping the equation balanced:

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

`(S/2)/color(red)((l + h)) - (lh)/color(red)((l + h)) = (wcolor(red)(cancel(color(black)((l + h)))))/cancel(color(red)((l + h)))`

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

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

We can also rewrite this as:

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

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

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