document.write( "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?
\n" ); document.write( "(b) If the sections are 1 ft and 5 ft long, will the sticks form a triangle?
\n" ); document.write( "(c) If you break the longer stick at an arbitrary point, what is the probability that they form a triangle? \n" ); document.write( "

Algebra.Com's Answer #787215 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The lengths of the two shorter sticks together must be greater than the length of the longest stick.

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

\n" ); document.write( "(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.

\n" ); document.write( "(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.)

\n" ); document.write( "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.

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