By applying the rule, the sum of two sides of a triangle must be greater than the third side, we get 10+12 > x =>
22 > x => x <22 and 10+x >12, => x > 12-10 =>x > 2 So x can take integer values between 3 and 21
But the problem states that x is the side of an acute-angled triangle. Therefore each angle < 90.
If we take one leg of the triangle as 10 and the other as 12, and the hypotenuse as x, then 12^2 + 10^2 < x^2 (since the angle has to be less than 90) i.e x^2 <244. So possible values of x^2 can be 9,16,25,36,49, 64,1,100,121,144,169, 196, 225 (13 values) The other possibility is x & 10 are the legs and 12 is the hypotenuse.
Then, x^2 +10^2 > 12^2 => x^2 > 144-100 => x^2 >44 ( Then x cannot take the values 9, 16, 25 & 36). Therefore, possible integer values of x satisfying the above conditions are 13-4 = 9 values. Hence Option C is the correct option