PQR is an equilateral triangle such that the vertices Q and R lie on the lines x+y=2 and x+y=72 respectively. If P lies between the two lines at a distance 4 from one of them then the length of side of equilateral triangle PQR is (in units)
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a
8
b
473
c
853
d
453
answer is B.
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Detailed Solution
From Figure cosθ=4a,cos120-θ=2acosθ=2cos120-θ =2cos120cosθ+2sin120sinθ =-cosθ+3sinθ2cosθ=3sinθtanθ=23Substitute the above value in cosθ=4a cosθ=4aa=4secθ =41+43 =473