Question
A house is at the center of the several flat paths which surround it: 4 straight paths that travel from the house 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 the distance from the house to the circular moat? 
Answer: Option B
:
B
Option(b)
Solution:Shortcut:- Using Assumption
Finding the total lengths of all the paths
Assuming radius of the circle =2
Straight paths= 2x4=8
Each side of the square = 2√2 x4=8√2
Circular moat perimeter= 4Π
q (Total) = 4( 2+2√2 + Π)
Distance from centre to the moat = 2
Look for 2 in the answer options. Answer is option (b)
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:
B
Option(b)
Solution:Shortcut:- Using Assumption
Finding the total lengths of all the paths
Assuming radius of the circle =2
Straight paths= 2x4=8
Each side of the square = 2√2 x4=8√2
Circular moat perimeter= 4Π
q (Total) = 4( 2+2√2 + Π)
Distance from centre to the moat = 2
Look for 2 in the answer options. Answer is option (b)
Was this answer helpful ?
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