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

Question

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

itsanujsingh · Answer

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

rvgmat12 · Answer

Root(3)/4*x^2 = 1/2(x+2x+3x)

x = 4root(3)

Harshjha001 · Answer

D.

Sum of perpendiculars from a point to all the sides of an equilateral triangle is equal to the height of the equilateral triangle .

(1+2+3) = (root(3) / 2) *(side(s) of eq triangle).
side (s) = 4 * root(3)

Crytiocanalyst · Answer

Key to solving the question is understanding the fact that the three triangles formed by the perpendiculars can be equalled to the area of the triangle

=1/2 *a (since all sides are equal ) * ( 1+2+3) = root3/ 4

=>1/2 *6*a = root 3/4

=>4*root3 =a

Therefore IMO D

TarunKumar1234 · Answer

Sqrt(3)/4* a^2 = 1/2*a*(1+2+3) or, a = 12/sqrt(3) = 4*sqrt(3) So, I think D.

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

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GMAT Problem Solving (PS) Questions

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

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