Question 1151077
flag poles A and B are both perpendicular to the ground. Wires from the top of one flagpole are connected to the bottom of the other flagpole such that the point where the wires intersect is 10 feet above the ground. If the height of both A and B are an integer number of feet, how many possible heights are there for A?
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Note that the distance between them is not relevant.
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Also, the height of the intersection is a*b/(a + b) - you can work that out or take my word for it.
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a*b/(a+b) = 10
1 obvious solution is a = b = 20.
It's also obvious that the height of both must be greater than 10 feet.
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a*b = 10a + 10b
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By trial and error (using Excel) the combinations are:
20 & 20
30 & 15
35 & 14
60 & 12
110 & 11
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---> 10 possible values, but 20 is a duplicate.
---> 9 different possible values for A (or B).