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# If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig

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If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig  [#permalink]

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21 Feb 2018, 01:12
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Difficulty:

15% (low)

Question Stats:

85% (01:22) correct 15% (01:49) wrong based on 64 sessions

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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:

2018-02-21_1019_003.png [ 11.56 KiB | Viewed 951 times ]

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Re: If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig  [#permalink]

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21 Feb 2018, 01:38
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:
2018-02-21_1019_003.png

PR=$$2*\sqrt{2}$$
Perimeter = $$4*\sqrt{2}+4$$
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Re: If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig  [#permalink]

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21 Feb 2018, 04:07
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:
2018-02-21_1019_003.png

right angle triangle 90-45-45 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  [#permalink]

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21 Feb 2018, 17:27
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 $$4+4\sqrt{2}$$.

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Re: If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig  [#permalink]

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22 Feb 2018, 00:41
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:
2018-02-21_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  [#permalink]

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26 Feb 2018, 10:47
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:
2018-02-21_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.

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Re: If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig   [#permalink] 26 Feb 2018, 10:47
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# If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig

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