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If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig
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21 Feb 2018, 00:12
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84% (01:22) correct 16% (01:49) wrong based on 62 sessions
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Re: If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig
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21 Feb 2018, 00:38



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Re: If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig
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21 Feb 2018, 03:07
Bunuel wrote: If QR = 2, then what is the perimeter of quadrilateral PQRS in the figure above? A. \(6\sqrt{2} + 4\) B. \(4\sqrt{2} + 4\) C. \(4\sqrt{2} + 2\) D. \(2\sqrt{2} + 2\) E. \(3\sqrt{2}\) Attachment: 20180221_1019_003.png right angle triangle 904545 ratio of sides 1:1:rt2 so side of equilateral traingle = 2 rt 2 perimited = 2+ 2 + 2rt2 + 2rt2 4rt2 + 4 (B) imo



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If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig
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21 Feb 2018, 16:27
Looks scary if you're inclined to hate geometry like myself, but quite simple when you remember rules and take good notes.
\(x^2+x^2=PR^2\), so \(2^2+2^2=8\)
From there, we know that \(PR=\sqrt{8}\). That can be simplified to \(2\sqrt{2}\).
Since all angles of triangle PRS = 60, we know that we have an equilateral triangle and all sides are a the same. We're looking for the perimeter of the whole quadrilateral, so side RS and SP will contribute to it. Those are both equal to PR, so we'll take 2 of those, or \(2*2\sqrt{2}\), or more simply, \(4\sqrt{2}\).
We're given that \(x=2\), and 2 of those contribute to the perimeter, so the final perimeter will be \(4+4\sqrt{2}\).
Answer choice B.



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Re: If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig
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21 Feb 2018, 23:41
Bunuel wrote: If QR = 2, then what is the perimeter of quadrilateral PQRS in the figure above? A. \(6\sqrt{2} + 4\) B. \(4\sqrt{2} + 4\) C. \(4\sqrt{2} + 2\) D. \(2\sqrt{2} + 2\) E. \(3\sqrt{2}\) Attachment: 20180221_1019_003.png Answer must be B as x=2 and triangle QRS is isosceles then 3rd side is 2root 2 so perimeter is sum of all the side 2 sides with 2root 2 and 2 sides with 2 length so total is 4root2+ 4



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Re: If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig
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26 Feb 2018, 09:47
Bunuel wrote: If QR = 2, then what is the perimeter of quadrilateral PQRS in the figure above? A. \(6\sqrt{2} + 4\) B. \(4\sqrt{2} + 4\) C. \(4\sqrt{2} + 2\) D. \(2\sqrt{2} + 2\) E. \(3\sqrt{2}\) Attachment: 20180221_1019_003.png Since triangle PQR is an isosceles right triangle, side PR = 2√2. Since triangle PRS is an equilateral triangle, PR = RS = PS = 2√2. So the perimeter of quadrilateral PQRS is 2 + 2 + 2√2 + 2√2 = 4 + 4√2. Answer: B
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