CTET 2 Math and Science Sep 2016 Paper

Let the third side of the right angled triangle be x.
Since, in a right angled triangle hypotenuse of the
triangle is the longest side of the triangle.
Also in a triangle the third side of the triangle cannot be greater than the sum of other two sides and cannot be less than the difference of the other two sides.
That is,
Here, two cases arises
Case-1, if x is the largest side, then it will be the hypotenuse of the right angled triangle.
Then, by Pythagoras theorem,
$\mathit{x}=\sqrt{{\left(17\right)}^2+{\left(15\right)}^2}$
$=22.67$
Case -2, if x is not the largest side, then 17 will be the hypotenuse of the right angled triangle
Then, by Pythagoras theorem,
${\left(17\right)}^2={\mathit{x}}^2+{\left(15\right)}^2$
${\mathit{x}}^2={\left(17\right)}^2-{\left(15\right)}^2$
$=\left(17-15\right)\left(17+15\right)$
$=2\times 32$
${\mathit{x}}^2=64$
$\mathit{x}=8$
Therefore, the only possibilities are B and C.