Solution:
As, \[\vartriangle ACD\text{ }\sim\text{ }\vartriangle BCA\]
We have,
\[Ar\left( \vartriangle ACD \right)/\text{ }Ar\left( \vartriangle BCA \right)\]
\[=\text{ }A{{D}^{2}}/\text{ }A{{B}^{2}}~=\text{ }{{5}^{2}}/{{8}^{2}}\]
So,
\[Ar\left( \vartriangle ACD \right)/\text{ }Ar\left( \vartriangle BCA \right)\]
\[=\text{ }25/64\]