Question

In order to determine the slant height of several pyramids, Marjorie used the surface area formula, `S = 1/2 pt + b` for the slant height, `t`. What equation would be the correct transformation of the surface area formula for `t`?

Answer 1

`t=(2(S-b))/p`

Explanation:

So we need to solve the equation for `t`.

First, subtract `b` from both sides.
`Scolor(red)(-b)=1/2ptcolor(green)(cancelcolor(black)(+b)cancelcolor(red)(-b))`
`S-b=1/2pt`

Then, multiply both sides by `2`.
`color(red)(2)times(S-b)=color(green)(cancelcolor(red)(2times)cancelcolor(black)(1/2))pt`
`2(S-b)=pt`

Finally, divide both sides by `p`.
`2(S-b)color(red)(dividep)=color(green)cancelcolor(black)ptcolor(green)cancelcolor(red)(dividep)`
`(2(S-b))/p=t`