IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

beethoven

THERe are 2 parallel lines at 1 unit distance apart . A point P is in between the 2 lines, at a distance F from one of the line. There are other two points Q,R each one on the two parallel lines, such that PQR is an equilateral triangle. find the length of the side of the triangle?????

nadeemoidu

Draw lines perpendicular to the given parallel lines from P and R.
Let a side of the triangle be x.
Now there are 3 right triangles ( formed by the traingle and lines) , so you can get an equation in x and f.
_________
I'm getting the answer as x= ( 2/

3 )

( f² - f + 1 )

nishant_88

nadeemoidu is correct

manoj_babu

ya the ans is 2/(3)^1/2[(f^2-f+1)]^1/2

manoj_babu

consider 2 ll lines be y=f n y=-(1-f) one f units away frm x axis n ll to it let Q be (0,f) lying on line y=f n let P be (p,o) lying on x axis, let x be the angle bt y axis n QR (let R(r,f-1)

nw tanx=r n tan(60+x)=p/f find tanx n 1+r^2=side^2=p^2+f^2

we know dat r=tanx compute side

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