to Q 4)

for triangle

sum of two sides>sum of third side

draw line a

dividin in 3 parts is same as choosing 2 points

now for x+y>z

the length of one side is always less than a/2

hence we choose point x from [0,a/2)

now from x we choose second point from (x,a/2+x] so that distance between last  points also <a/2

 

so probability

=(a/2)(a/2)/a*a

=1/4