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In the figure above, each of the four squares

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In the figure above, each of the four squares [#permalink] New post 06 Jan 2017, 07:52
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42% (01:08) correct 57% (00:00) wrong based on 7 sessions
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In the figure above, each of the four squares has sides of length x. If \(\triangle\)\(PQR\) is formed by joining the centers of three of the squares, what is the perimeter of \(\triangle\)\(PQR\) 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, each of the four squares [#permalink] New post 06 Jan 2017, 08:18
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Explanation.

P is the center of square and so is Q. From P to edge the square of is \(\frac{x}{2}\). And from edge of square to Q is \(\frac{x}{2}\) as well.

So PQ = x
Similarly QR is also equal to x.

Again P to edge of the square is half of the length of diagonal \(\frac{1}{2}\sqrt{2}x\). Again from corner to R is also \(\frac{1}{2}\sqrt{2}x\).

PR =\(2 \times \frac{1}{2}\sqrt{2}x\)= \(\sqrt{2}x\).


Hence perimeter = PQ + QR + PR = \(x + x + \sqrt{2}x\) = \(2x + \sqrt{2}x\)

Hence option E is correct.
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Re: In the figure above, each of the four squares   [#permalink] 06 Jan 2017, 08:18
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In the figure above, each of the four squares

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