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If PQ = 1, what is the length of RS

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If PQ = 1, what is the length of RS [#permalink] New post 06 Aug 2017, 10:55
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Attachment:
triangle.jpg
triangle.jpg [ 19.78 KiB | Viewed 876 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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Re: If PQ = 1, what is the length of RS [#permalink] New post 27 Jun 2018, 11:19
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. \(\frac{2}{\sqrt{12}}\)


Any explanation for the answer?
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Re: If PQ = 1, what is the length of RS [#permalink] New post 04 Jul 2018, 07:25
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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
FIG 1.jpg [ 17.51 KiB | Viewed 246 times ]


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Re: If PQ = 1, what is the length of RS   [#permalink] 04 Jul 2018, 07:25
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