Problem of the Week
Problem C
Three Triangles

The right-angled triangle $\mathrm{△}ABC$ has $\mathrm{\angle }ABC=90\mathrm{°}$ and $AB=12$. Point $D$ is on side $BC$ such that $BD=5$ and the area of $\mathrm{△}ADC$ is $80\mathrm{\%}$ of the area of $\mathrm{△}ABD$.

Determine the perimeter of $\mathrm{△}ADC$.

Note: You may find the following useful:

The Pythagorean Theorem states, "In a right-angled triangle, the square of the length of hypotenuse (the side opposite the right angle) equals the sum of the squares of the lengths of the other two sides."

In the right-angled triangle shown, $c$ is the hypotenuse, $a$ and $b$ are the lengths of the other two sides, and $c^2=a^2+b^2$.

Theme: Geometry & Measurement