bhushan252 wrote:
OA B
let distance from the castle to the circular moat is x
distance from 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 ( addition of lenght of diagonals of sqr)= 4x
Thus side of inscribed sqr = x*sqrt2 (use pythagoras 2x^ = (side of sqr)^2.....hence perimeter of sqr = 4*sqrt2*x
circumference of perimeter = pi * (2*x)
Thus our eqn becomes => q= pi * (2*x) + 4*sqrt2*x + 4x
on simplification we get x = q / 2(2+2*sqrt(2)+pi) km...OA B
Strange, this problem seems to have a different answer when we take the side of the square to be a ( or r) or may be I am doing something wrong!
Here, what I am doing -
Let the side of the sq be a, then sum of four sides = 4a;
Using formula, diag of a sq is sqrt(2)a, we get sum of the paths four paths from castle to moat ( i.e, sum the diagonals) as = 2a sqrt(2) ;
Circumference of the circle as 2pie a sqrt(2)/2
Putting it all together we
4a +2asqrt(2) +2pie sqrt(2)/2 = q
=> 4a +2asqrt(2) +pie asqrt(2) =q
=> sqrt(2)a (2 sqrt(2)+2 +pie) = q
=> a = q/sqrt(2) (2 sqrt(2)+2 +pie)
Can anybody shed some more light on this..?