SOLUTION: 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

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Question 1158597: 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?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

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%2Bb%3Ec ->2%2B3%3E4->5%3E4 ->true
a%2Bc%3Eb ->2%2B4%3E3->6%3E3-> true
b%2Bc%3Ea ->3%2B4%3E2->7%3E2 ->true
=> 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%2Bb%3Ec ->1%2B5%3E4->6%3E4-> false
a%2Bc%3Eb ->1%2B4%3E5->5%3E5 ->false
b%2Bc%3Ea ->5%2B4%3E1->9%3E1-> true
since two false => 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%2F6 or r approximately 16.67%