A rod of length l is to be divided into two parts, such that if 5 times the smaller portion is added to half of the larger portion, it always be less than l. This can be achieved by taking length of the larger portion more than
Answers
Let's say the length of the stick is l. You break it into two pieces with lengths x and y, thus making the length of the third piece (l-x-y).
Now, let's consider this diagram.
The area of the triangle formed by the axes and the line x+y= l corresponds to all the possibilities of breaking the stick into three parts i.e. x,y>0 & x+y<l.
Now, for the three pieces to form the sides of a triangle, the triangle equality should be true.
x+y>l-x-y ⇒ x+y> l/2.
x+l-x-y>y ⇒ y<l/2
y+l-x-y>x⇒ x<l/2
The shaded area in the figure above corresponds to all the three conditions above.
probability = favorable outcome / all possible outcomes
= shaded area/ total area
= (1/2 *l/2*l/2)/1/2 *l*l
= 1/4
I hope this will help you
If not then comment me
