Consider the parallelogram in figure, where $d=\overline{DB}=15$ and $a=\overline{AH}=6$. Furthermore, assume that $\widehat{ADB}$ is a right angle. Find the perimeter.
My solution:
let's call $h=\overline{DH}$ and $b=\overline{HB}$, then
$$
a:h=h:b\implies h^2=ab\\
h^2+b^2=d^2 \implies b^2+ab-d^2=0
$$
the last one is a quadratic equation in the unknown $b$. From now on it is easy to procede.
Now, my question: there is a simpler solution, for a 12 year old student that still don't know quadratic equations?