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In the figure above

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In the figure above [#permalink] New post 18 Mar 2018, 09:44
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In the figure above, each of the four squares has sides of length x. If ∆PQR is formed by joining the centers of three of the squares, what is the perimeter of ∆PQR in terms of x ?

(A) \(2x \sqrt{2}\)

(B) \(\frac{x\sqrt2}{2}\) \(+ x\)

(C) \(2x + \sqrt{2}\)

(D) \(x \sqrt{2} + 2\)

(E) \(2x + x \sqrt{2}\)
[Reveal] Spoiler: OA

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Re: In the figure above [#permalink] New post 23 Mar 2018, 08:10
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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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Re: In the figure above   [#permalink] 23 Mar 2018, 08:10
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