Discussion

Explanation:

We know in any triangle sum of two sides is always greater that the third side.

Also, for an obtuse angled triangle square of the longest side is greater than sum of square of the two shorter sides.

Case I: Let 14 be the largest side. 
⇒ 7 + x > 14
⇒ x > 7

Also, 142 > 72 + x2
⇒ x2 < 196 – 49
⇒ x2 < 147
⇒ x < √147

⇒ x = 8 or 9 or 10 or 11 or 12

Case II: Let x be the largest side. 
⇒ 7 + 14 > x
⇒ x < 21

Also, x2 > 72 +142
⇒ x2 > 196 + 49
⇒ x2 > 245
⇒ x > √245

⇒ x = 16 or 17 or 18 or 19 or 20

∴ x can take 10 integral values.

Hence, 10.

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