The three sides of an acute angled triangle (all in cms) are 12, 19 and h. How many integer values can h take? Choose the correct choice from the following choices.
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 h can be when it is the hypotenuse of the triangle.   So, h= sqrt(12^2 + 19^2) = 22.5 (approx)   The maximum length of h can be when side of length 12 is the hypotenuse of the triangle.   So, h = sqrt (19^2 - 12^2) = 14.7 (approx)   So, h&gt;14.7 and h&lt;22.5.   Hence, possible values for h 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 h. How many integer values can h take?