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If PQ = 1, what is the length of RS [#permalink]
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Attachment: #GREpracticequestion If PQ=1PQ=1, what is the length of RS.jpg [ 19.78 KiB | Viewed 1552 times ]

If $$PQ = 1$$, what is the length of $$RS$$

A. $$\frac{1}{12}$$

B. $$\frac{\sqrt{3}}{12}$$

C. $$\frac{1}{6}$$

D. $$\frac{2}{3 \sqrt{3}}$$

E. $$\frac{2}{\sqrt{12}}$$
[Reveal] Spoiler: OA

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Intern Joined: 14 Jun 2018
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Re: If PQ = 1, what is the length of RS [#permalink]
Carcass wrote:

If PQ = l, what is the length of RS

A. $$\frac{1}{12}$$

B. $$\frac{\sqrt{3}}{12}$$

C. $$\frac{1}{6}$$

D. $$\frac{2}{3 \sqrt{3}}$$

E. $$\frac{2}{\sqrt{12}}$$ VP Joined: 20 Apr 2016
Posts: 1302
WE: Engineering (Energy and Utilities)
Followers: 22

Kudos [?]: 1342  , given: 251

Re: If PQ = 1, what is the length of RS [#permalink]
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Carcass wrote:

If $$PQ = 1$$, what is the length of $$RS$$
A. $$\frac{1}{12}$$

B. $$\frac{\sqrt{3}}{12}$$

C. $$\frac{1}{6}$$

D. $$\frac{2}{3 \sqrt{3}}$$

E. $$\frac{2}{\sqrt{12}}$$

Here PQ = 1

Plz see the diagram attached.

Now △ PQT,

∠QPT = 30° , ∠QTP = 90° and ∠PQT = 60°

so it is a 30° - 60° -90° and we know the sides are distributed in the ratio $$1 : \sqrt3 : 2$$

Now PQ = 1,
so $$QT = \frac{1}{2} and PT = \frac{2}{sqrt3}$$

Now let us consider △ QTS

∠TQS = 30° , ∠QST = 60° and ∠QTS = 90°

so it is a 30° - 60° -90° and we know the sides are distributed in the ratio $$1 : \sqrt3 : 2$$

Now $$QT = \frac{1}{2}$$,
so $$QS = \frac{1}{\sqrt3} and TS = \frac{1}{2\sqrt3}$$

Now let us consider △ TRS

∠RST = 60° , ∠RTS = 30° and ∠TRS = 90°

so it is a 30° - 60° -90° and we know the sides are distributed in the ratio $$1 : \sqrt3 : 2$$

Now $$TS = \frac{1}{2\sqrt3}$$,
so $$RT = \frac{1}{4} and RS = \frac{1}{4\sqrt3}$$.

But $$RS = \frac{1}{4\sqrt3}$$ can also be written as $$RS = \frac{1}{4\sqrt3} *\frac{\sqrt3}{\sqrt3} = \frac{\sqrt3}{12}$$
Attachments FIG 1.jpg [ 17.51 KiB | Viewed 1885 times ]

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