ABC is a triangle with sides $AB = 6 m$, $BC = 8m$, and $AC = 10m$. A line $k$ in the plane of the triangle $ABC$ moves along the segment $AC$ at the rate of $1cm$ per sec. The line starts at A and ends at $C$ and is always perpendicular to $AC$.
- How long does it take the line to reach the point B?
- How long does it take the line to bisect the area of the triangle?
- What is the area of the region that the line sweeps in its movement after $6$ min and $45$ sec?
- What is the area of the region that the line sweeps at any give moment from the start of its movement?
I have noticed that $(6,8,10)$ are Pythagorean triple and have solved the first question (6 mints is the answer), but the last three seems a bit tedious, could somebody tell me which could be the most easiest approach to solve these three?