What is the probability that 3 pieces make a triangle?

Question

Mathematics

Eden Day

14 December, 21:08

What is the probability that 3 pieces make a triangle?

+5

Answers (1)

Know the Answer?

Heather Downs · Answer 1

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
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
y+l-x-y>x⇒ x
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