Any side of triangle is less than the sum of other two sides so in this case \(x < 22.\)
Also any side of triangle is larger than positive difference of other two sides so \(x > 2\).
\(2 < x < 22\)
Total of \(19\) possible values.

Given that the triangle is acute, hence

\(AB^2 + BC^2 > AC^2\)

Case 1:-
\(10^2 + x^2 > 12^2\)
\(x^2 > 144 - 100 = 44\)
hence, \(x^2 > 44\) means.... \(x>6\)

Case 2:-
\(10^2 + 12^2 > x^2\)
\(x^2 < 244\)
\(x<16\)

hence \(x = 7,8,9,10,11,12,13,14,15 => 9 \) triangles
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