What is tan 11pi divided by 6

Do you mean tan(11pi)/6 or tan(11pi/6)?

tan(11pi)/6=0.1147933459688

tan(11pi/6)=0.1008637210658

We are essentially looking for the LCM (least common multiple) of the lengths 25, 40 and 50 cm.

Since 50 is already a common multiple of 25, since 2*25=50, we only need to look for the LCM of 40 and 50.

One simple way to find the LCM is to factor both numbers,
40=2^3*5
50=2*5^2
and look for the product of the higher power of each factor, which in this case is 2^3*5^2=8*25=200.

Another way, looks round about in this case, is to look for the HCF, which is the product of the lowest power of each factor, which in this case is 2*5=10.
The LCM is then the product of the two numbers divided by the HCF, or
LCM=50*40/10=200, again.