25 Apr '13 09:22

Triangle first..

* I have a stick one meter long, reaching from point A to D. I break it at two mutually independent spots and call those B and C, with B closer to A than to D, and then try to form the triangle with side length AB, BC, and CD. Find the likelihoods that

* I can't form a triangle at all (e.g. side length 1 cm, 1 cm, 98 cm)

* I get an acute angle triangle,

* I get an obtuse angle triangle.

* instead of a stick I use a rope, one meter long, tied as a closed loop. I mark two points along it, pull the rope taut between those points, and then try to pull the rest of the rope also taut so I'd get a triangle with a perimeter length equal to that of the rope. What are the likelihoods now for no triangle, acute angle triangle, and obtuse angle triangle?

* I have a trapezoid ABCD with a perimeter length of one meter. One of the sides is 35 cm long and another 25 cm long. How long can the other two sides be?

* I have a stick one meter long, reaching from point A to D. I break it at two mutually independent spots and call those B and C, with B closer to A than to D, and then try to form the triangle with side length AB, BC, and CD. Find the likelihoods that

* I can't form a triangle at all (e.g. side length 1 cm, 1 cm, 98 cm)

* I get an acute angle triangle,

* I get an obtuse angle triangle.

* instead of a stick I use a rope, one meter long, tied as a closed loop. I mark two points along it, pull the rope taut between those points, and then try to pull the rest of the rope also taut so I'd get a triangle with a perimeter length equal to that of the rope. What are the likelihoods now for no triangle, acute angle triangle, and obtuse angle triangle?

* I have a trapezoid ABCD with a perimeter length of one meter. One of the sides is 35 cm long and another 25 cm long. How long can the other two sides be?