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?

Options:

A . q4√2+2√2+π km

B . q2(2+2√2+π) km

C . q2+2√2+π km

D . 2q2+2√2+π km

E . 1334

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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