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# The figure above shows squares PQRS and TUVW, each with side of length

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Math Expert
Joined: 02 Sep 2009
Posts: 47200
The figure above shows squares PQRS and TUVW, each with side of length  [#permalink]

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04 Oct 2017, 00:31
00:00

Difficulty:

55% (hard)

Question Stats:

66% (01:20) correct 34% (01:32) wrong based on 38 sessions

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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 610 times ]

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

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04 Oct 2017, 07:53
1
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
Re: The figure above shows squares PQRS and TUVW, each with side of length &nbs [#permalink] 04 Oct 2017, 07:53
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