SOLUTION: 884.One stick is 3 ft long and another is 6 ft long. You break the longer stick into sections. (a) If the sections are 2 ft and 4 ft long, will the sticks form a triangle? (b) If

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 884.One stick is 3 ft long and another is 6 ft long. You break the longer stick into sections. (a) If the sections are 2 ft and 4 ft long, will the sticks form a triangle? (b) If       Log On

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Question 1163207: 884.One stick is 3 ft long and another is 6 ft long. You break the longer stick into sections. (a) If the sections are 2 ft and 4 ft long, will the sticks form a triangle?
(b) If the sections are 1 ft and 5 ft long, will the sticks form a triangle?
(c) If you break the longer stick at an arbitrary point, what is the probability that they form a triangle?
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
One stick is 3 ft long and another is 6 ft long. You break the longer stick into sections.
(a) If the sections are 2 ft and 4 ft long, will the sticks form a triangle?
The longest side, 4 ft, must be longer than the difference between the lengths of the other 2 sides, and shorter than the sum of the other 2 sides.
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(b) If the sections are 1 ft and 5 ft long, will the sticks form a triangle?
The longest side, 4 ft, must be longer than the difference between the lengths of the other 2 sides, and shorter than the sum of the other 2 sides.
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(c) If you break the longer stick at an arbitrary point, what is the probability that they form a triangle?

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The lengths of the two shorter sticks together must be greater than the length of the longest stick.

(a) The three sticks are now 2, 3, and 4 feet long. 2+3=5 is greater than 4; yes, you get a triangle.

(b) The three sticks are now 1, 3, and 5 feet long. 1+3=4 is less than 5; no, you don't get a triangle.

(c) Either with logical analysis, or with formal algebra, you can determine that the 6-foot stick can be cut at anywhere from 1.5 feet to 4.5 feet from one end to have the three sticks form a triangle (because the difference between 1.5 feet and 4.5 feet is 3 feet -- the length of the other stick.)

The range of where the cut can be made is then 4.5-1.5=3 feet; and the full length of the second stick is 6 feet. So the probability that the second stick gets cut in a way that makes it possible to form a triangle is 3/6 = 1/2.