We are given
[tex]2ab + 2bc + 2ac = 350 \iff ab + bc + ac = 175[/tex]
We are also given [tex]a=b[/tex] and [tex]c=9[/tex], which allows us to rewrite the equation as
[tex]a^2 + 9a + 9a = 175 \iff a^2+18a-175=0[/tex]
(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.
