The perimeter of the triangle formed by the points

We have a triangle whose co-ordinates are A (0, 0); B (1, 0); C (0, 1). So clearly the triangle is right angled triangle, right angled at A. So,

$\mathrm{AB}=1$ unit

$\mathrm{AC}=1$ unit

Now apply Pythagoras theorem to get the hypotenuse,

$\mathrm{BC}=\sqrt{\mathrm{AB}^{2}+\mathrm{AC}^{2}}$

$=\sqrt{2}$

So the perimeter of the triangle is,

$=\mathrm{AB}+\mathrm{BC}+\mathrm{AC}$

$=1+1+\sqrt{2}$

$=2+\sqrt{2}$

Therefore the answer is (d)