aykutkaraalioglu wrote:A castle is at the center of the several flat paths which surround it: 4 straight paths that travel from the castle to its circular moat, where they meet up with a perfectly circular path which borders the moat; that circular path circumscribes a square path which has its corners at the ends of the 4 straight paths-see the diagram to the right. If the total length of all of the pathways is q kilometers, then which expression represents distance from the castle to the circular moat?
A) q / 4(2+2√2)+π) km
B) q / 2(2+2√2)+π) km
C) q / (2+2√2+π) km
D) 2q / (2+2√2+π) km
E) 4q / (2+2√2+π) km
When you post a question, please include the answer choices.
We can plug in values as follows:
q = the sum of all of the lengths = 4(10) + 4(10√2) + 20π = 40 + 40√2 + 20π.
The distance from the center to the circular moat = 10. This is our target.
Now we plug into the answer choices q = 40 + 40√2 + 20π to see which yields our target of 10.
Only answer choice
B works:
q / 2(2+2√2)+π)
= (40+40√2+20π) / 2(2+2√2+π)
= 20(2+2√2+π) / 2(2+2√2+π)
= 10.
The correct answer is
B.
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