How far from the base of the house do you need to place a 15' laddder so that it exatly reaches tehe top of a 12' wall?
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First, , and if we multiply
by
we get
Subtracting this from the numerator gives a remainder of
Next, , and if we multiply
by
we have
and subtracting this from the previous remainder, we end up with a new remainder of
Next, , and if we multiply
by
we get
Subtracting from the previous remainder, we get a new remainder of
which contains no more factors of , so we're done.
So,