<PRE><B>Question 1158597</B>

One stick is {{{3ft}}} long and another is {{{6ft}}} long. You break the longer stick into sections.


 (a) If the sections are {{{2ft}}} and {{{4ft}}} long, will the sticks form a triangle?

{{{a=2 }}}
{{{b=3 }}}
{{{c=4}}}

recall: The Triangle Inequality Theorem states that the {{{sum}}} of any {{{2}}} sides of a triangle {{{must}}} be greater than the measure of the {{{third }}}side.

so,
{{{a+b&gt;c}}} -&gt;{{{2+3&gt;4}}}-&gt;{{{5&gt;4}}} -&gt;true
{{{a+c&gt;b}}} -&gt;{{{2+4&gt;3}}}-&gt;{{{6&gt;3}}}-&gt; true
{{{b+c&gt;a}}} -&gt;{{{3+4&gt;2}}}-&gt;{{{7&gt;2}}} -&gt;true

=&gt; the sticks {{{will}}} form a triangle

(b) If the sections are {{{1ft}}} and {{{5ft}}} long, will the sticks form a triangle?
{{{a=1 }}}
{{{b=5 }}}
{{{c=4}}}
{{{a+b&gt;c}}} -&gt;{{{1+5&gt;4}}}-&gt;{{{6&gt;4}}}-&gt; false
{{{a+c&gt;b}}} -&gt;{{{1+4&gt;5}}}-&gt;{{{5&gt;5}}} -&gt;false
{{{b+c&gt;a}}} -&gt;{{{5+4&gt;1}}}-&gt;{{{9&gt;1}}}-&gt; true

since two false =&gt; the sticks will {{{not}}} form a triangle


(c) If you break the longer stick at an arbitrary point, what is the probability that they form a triangle?

 the probability that they form a triangle is {{{1/6}}} or r approximately {{{16.67}}}%

</PRE>