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# Point P is inside equilateral triangle ABC. Points Q, R, and S are the

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Math Expert
Joined: 02 Sep 2009
Posts: 54385
Point P is inside equilateral triangle ABC. Points Q, R, and S are the  [#permalink]

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26 Mar 2019, 23:26
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Difficulty:

35% (medium)

Question Stats:

86% (02:26) correct 14% (03:33) wrong based on 7 sessions

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Point P is inside equilateral triangle ABC. Points Q, R, and S are the feet of the perpendiculars from P to AB, BC, and CA, respectively. Given that PQ=1, PR=2, and PS=3, what is AB?

(A) 4
(B) $$3\sqrt{3}$$
(C) 6
(D) $$4\sqrt{3}$$
(E) 9

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Joined: 27 Sep 2018
Posts: 37
Re: Point P is inside equilateral triangle ABC. Points Q, R, and S are the  [#permalink]

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27 Mar 2019, 00:24
1
Area of Triangle ABC= rt3/4 * a^2
where a = side of equailateral trianfle

Also, Area of Triangle ABC= Ar of traingle (PAB+PBC+PCA)
rt3/4 8a^2= 1/2*1*a+1/2*2*a+1/2*3*a
Solving we get a=4rt3
Re: Point P is inside equilateral triangle ABC. Points Q, R, and S are the   [#permalink] 27 Mar 2019, 00:24
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# Point P is inside equilateral triangle ABC. Points Q, R, and S are the

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