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?
![Click to Enlarge Image A House Is At The Center Of The Several Flat Paths Which Sur...](https://lakshyaeducation.in/quizpics/quiz/e3edf286a153adf65c83de429c52c97a634983483649356574_7052978.png)
Answer: Option B
:
B
Option(b)
Solution:Shortcut:- Using Assumption
![Click to Enlarge Image A House Is At The Center Of The Several Flat Paths Which Sur...](https://tnl-content-images.s3-us-west-2.amazonaws.com/xml-migration/789235bfa50536ec4a0d588d28b4e1a316-4-11-8-rid8.png)
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
![Click to Enlarge Image A House Is At The Center Of The Several Flat Paths Which Sur...](https://tnl-content-images.s3-us-west-2.amazonaws.com/xml-migration/789235bfa50536ec4a0d588d28b4e1a316-4-11-8-rid8.png)
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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