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Math Expert V
Joined: 02 Sep 2009
Posts: 58398
The figure above shows squares PQRS and TUVW, each with side of length  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 71% (02:09) correct 29% (02:06) wrong based on 48 sessions

HideShow timer Statistics The figure above shows squares PQRS and TUVW, each with side of length 6, that lie on line n. If RM = MW, then RW =

(A) 2√3
(B) 6
(C) 4√3
(D) 6√2
(E) 10

Attachment: 2017-10-04_1121_001.png [ 9.08 KiB | Viewed 967 times ]

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Retired Moderator D
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
Re: The figure above shows squares PQRS and TUVW, each with side of length  [#permalink]

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Bunuel wrote: The figure above shows squares PQRS and TUVW, each with side of length 6, that lie on line n. If RM = MW, then RW =

(A) 2√3
(B) 6
(C) 4√3
(D) 6√2
(E) 10

Attachment:
2017-10-04_1121_001.png

Need to find $$RW=2RM$$

In triangle QRM & TMW, $$QR=TW$$, $$RM=MW$$ and angle $$QRM=TWM=90°$$. Hence both the triangles are congruent

This implies angle $$QMR=TMW=60°$$. Hence triangle QRM is a $$30°-60°-90°$$ triangle so the ratio of sides will be $$1:\sqrt{3}:2$$

As $$QR=6$$, so $$RM=\frac{6}{\sqrt{3}}$$ $$=2\sqrt{3}$$

Hence $$RW=2*2\sqrt{3}=4\sqrt{3}$$

Option C
Non-Human User Joined: 09 Sep 2013
Posts: 13385
Re: The figure above shows squares PQRS and TUVW, each with side of length  [#permalink]

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_________________ Re: The figure above shows squares PQRS and TUVW, each with side of length   [#permalink] 06 Mar 2019, 10:10
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