ardz24 wrote:A 5 meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point?
A) 1/6
B) 1/5
C) 3/10
D) 1/3
E) 2/5
Let the wire from left to right be composed of 5 dashes, implying that the length of each dash is 1 meter:
-----
Case 1:
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If a cut is made anywhere in the blue portion, the length of the remaining wire will be greater than 4 meters, allowing us to form a square with an area greater than 1.
Since the blue portion constitutes 1/5 of the wire, P(cut in the blue portion) = 1/5.
Case 2:
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If a cut is made anywhere in the red portion, the length of the remaining wire will be greater than 4 meters, allowing us to form a square with an area greater than 1.
Since the red portion constitutes 1/5 of the wire, P(cut in the red portion) = 1/5.
Since a favorable outcome will be yielded by Case 1 OR Case 2, we ADD the probabilities:
P(square with an area greater than 1) = 1/5 + 1/5 = 2/5.
The correct answer is
E.
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