The three sides of an acute angled triangle (all in cms) are 12, 19 and x. How many integer values can x take?
Answers:	A) 23	B) 22	C) 15	D) 8	E) 7
In acute angle triangles all angles in the triangle should be less than 90.   The maximum length of x can be when it is the hypotenuse of the triangle.   So, x= sqrt(12^2 + 19^2) = 22.5 (approx)   The maximum length of x can be when side of length 12 is the hypotenuse of the triangle.   So, x = sqrt (19^2 - 12^2) = 14.7 (approx)   So, x&gt;14.7 and x&lt;22.5.   Hence, possible values for x can be 15,16,17,18,19,20,21 and 22. Total 8 values.   Answer 8.
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The three sides of an acute angled triangle (all in cms) are 12, 19 and x. How many integer values can x take?