If in any triangle, the angles are in the ratio of 1 : 2 : 1, then what will be the ratio of its sides?

Given, ratio of the angles of the triangle = 1 : 2 : 1

Let the angles of the traiangle are 1p, 2p ,1p respectively

$$=$$>  1p + 2p + 1p = 180$$^{\circ\ }$$

$$=$$>  4p = 180$$^{\circ\ }$$

$$=$$>  1p = 45$$^{\circ\ }$$

$$\therefore\ $$The angles of the triangle are 45$$^{\circ\ }$$, 90$$^{\circ\ }$$, 45$$^{\circ\ }$$

The triangle is a isosceles right angled triangle

$$=$$>  The ratio of the sides of the triangle are $$1 : \sqrt 2 : 1$$

Hence, the correct answer is Option C