To determine the number of obtuse angled triangles with sides 8cm, 15cm, and xcm, we need to identify the range of possible values for x that would result in an obtuse triangle.
In an obtuse triangle, the square of the largest side is greater than the sum of the squares of the other two sides.
Let's consider the given triangle with sides 8cm, 15cm, and xcm:
Using the Pythagorean Theorem, we can determine that the largest side is the hypotenuse. So, we have:
$x^2 > 8^2 + 15^2$
Simplifying the equation:
$x^2 > 64 + 225$
$x^2 > 289$
Taking the square root of both sides:
$x > \sqrt{289}$
$x > 17$
Thus, any integer value of x greater than 17 would result in an obtuse triangle.
The range of possible integer values for x is from 18 and onwards.
To find the number of obtuse angled triangles with sides 8cm, 15cm, and xcm, where x is an integer greater than 17, we subtract 17 from the total number of integers greater than 17.
The number of obtuse angled triangles is given by:
$10 - 17 = -7$
Since negative values are not possible, the number of obtuse angled triangles in this case is 0.
Therefore, the correct answer is C) 10.