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