Let sides of isosceles triangle are 3x,3x and 4x.

Then, half-perimeter (s) = \( \Large \frac{a+b+c}{2} \)

= \( \Large \frac{3x+3x+4x}{2} \)=5x

Given, area of isosceles triangle

= \( \Large 18\sqrt{5} \)sq units

\( \Large \sqrt{s(s-a)(s-b)(s-c)}=18\sqrt{5} \)

\( \Large \sqrt{5x(5x-3x)(5x-3x)(5x-4x)}=18\sqrt{5} \)

\( \Large \sqrt{5x\times 2x\times 2x\times x}=18\sqrt{5} \)

=> \( \Large 2\sqrt{5}x^{2}=18\sqrt{5} \)

=> \( \Large x^{2}=9 \)

=> x=3

Third side of isosceles triangle

=\( \Large 4\times 3 \)= 12units