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Question

ABC is an equilateral triangle with side length k such that the vertices B and C lie on two parallel lines at a distance of 9 units. If A lies between the parallel lines at a distance of 5 units from one of them, then the value of [k] is
([.] denotes the greatest integer function)

A
7
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B
8
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C
9
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D
10
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Solution

The correct option is C 9

From diagram,
cosθ=4k, sinθ=k216k
cos(120θ)=5kcos120cosθ+sin120sinθ=5k12×4k+32×k216k=5k32×k216k=7kk216k=14k33k248=196k=2443=81.33[k]=9

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