a²+b²=0.5²
ra+b=6
a+rb=8
1)
2)
3)
Rearrange 2) to get b=6-ra and substitute this into 3) to get
4)
Rearrange 3) to get a=8-rb and substitute this into 2) to get
5)
Substitute 4) and 5) into 1) to get
r4-402r2+768r-399=0
6)
This can be solved numerically using the Newton-Raphson method; the solution is r=19.0467. Substitute this into 4) and 5) to arrive at -
a=0.2938
ra=5.596m
b=0.4046
rb=7.706m
=> length of plank is 9.524m by Pythagoras.
Why is the previous method wrong?