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

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Answer 1 · 2018-01-05T15:02:48

$t = \frac{2 (S - b)}{p}$ $t=(2(S-b))/p$

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

First, subtract $b$ $b$ 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 $p$ .
$2(S-b)color(red)(dividep)=color(green)cancelcolor(black)ptcolor(green)cancelcolor(red)(dividep)$
$(2(S-b))/p=t$

In order to determine the slant height of several pyramids, Marjorie used the surface area formula, S = 1/2 pt + bS=12pt+bS = 1/2 pt + b for the slant height, ttt. What equation would be the correct transformation of the surface area formula for ttt?