AMO 2027 Grades 8-9 SET 14 - Self-study Question 10

Question 3. Triangle $ABC$ is a right triangle with $AB=60$ units, $AC=80$ units and $BC=100$ units. $D$ is a point between $B$ and $C$ such that $\triangle ADB$ and $\triangle ADC$ have equal perimeters. Find the length of the side $BD$.