http://codeforces.com/problemset/problem/794/B
Basic properties of triangle
The total area of triangle is ½*(basehight)=h/2. So after deviding it in n parts of equal area ,area of each part=h/(2n)
Now let the first cut be at height x from apex thus by using similiarity of triangle the base of small triangle(b) will be
x/b=h/1 {since base of bigger triangle is 1}
So, b=x/h
Thus , area =h/(2*n)
, ½*(x/h)(x) =h/(2*n)
=> x=h*sqrt(1/n)
Generally,
For k’th cut , we can say that area of triangle from apex to that cut will be equal to sum of k pieces which is equal to k times of individual area,
So,
½*(x/h)(x) =k*h/(2*n)
=> x=h*sqrt(k/n)