Question

The surface area for a rectangular prism is given by the formula SA = 2ab + 2bc + 2ac, where a, b, and c are the lengths of the
prism
If the surface area of a rectangular prism with side c measuring 9 meters is 350 square meters and length of side a measuring the
same length as side b, then what is the length of side a of the rectangular prism?

Answer 1

We are given

$2ab + 2bc + 2ac = 350 \iff ab + bc + ac = 175$

We are also given $a=b$ and $c=9$, which allows us to rewrite the equation as

$a^2 + 9a + 9a = 175 \iff a^2+18a-175=0$

(I substituted every "b" with "a" and every "c" with "9").

The solutions to this quadratic equation are -25 and 7. We discard -25 because a side with negative length would make no sense.