Every 1/2 foot wide vertical boards is arranged 3 feet apart and the total distance covered is 42 1/2 foot.If x is the number of vertical boards, we would have (x-1) 3 feet distances.

So we can form the equation,

\(\frac{1}{2}*x + 3*(x-1) = 42\frac{1}{2}\)

\(\frac{x}{2} + (3x - 3) = 42\frac{1}{2}\)

\(\frac{x + 2(3x - 3)}{2} = \frac{85}{2}\)

\(\frac{x + 6x - 6}{2} = \frac{85}{2}\)

Multiplying by 2,

\(7x - 6 = 85\)

\(7x = 91\)

\(x = 13\)

Therefore, the number of vertical boards is

13(Option D)
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