Given,

each of the square are of side x imagine a point \(a\) between P and Q such that the point is intersected by a side of the square and point \(b\) between Q and R such that it is also intersected by a side of the square

Now distance between P to a = distance between a to Q. If a side of the square has length \(x\) then distance between p to a is half of it hence \(\frac{x}{2}\) similarly distance between a to Q is also \(\frac{x}{2}\) therefore total distance between P to Q is \(\frac{x}{2} * 2 =x\)

Similar conclusion can be made for the distance Q and R going through point \(b\) and hence distance between Q and R is also \(x\)

This triangle is an Isosceles right triangle therefore sides are in the ratio \(x: x: x\sqrt{2}\)

Hence, perimeter = \(x + x + x\sqrt{2}\)

option E

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This is my response to the question and may be incorrect. Feel free to rectify any mistakes