Question

The perimeter of a triangle formed by points $(0,0),(6,0),(0,6)$ is

• A. $6(2+\sqrt{2})$ units
• B. $2+\sqrt{2}$ units
• C. $6\sqrt{2}$ units
• D. None of the above

Answer 1

The correct option is A $6(2+\sqrt{2})$ units

Let the co-ordinates of the given points be as follows:

$O(0,0)$; $A(6,0)$ and $B(0,6)$

By distance formula, $OA=\sqrt{(6-0{)}^2+(0-0{)}^2}$

$OA=\sqrt{6^2}=6$

$AB=\sqrt{(0-6{)}^2+(6-0{)}^2}$

$=\sqrt{36+36}=\sqrt{72}=$$6\sqrt{2}$

$OB=\sqrt{(0-0{)}^2+(6-0{)}^2}$

$OB=\sqrt{6^2}=6$

Perimeter $=OA+AB+OB$
$=6+6+6\sqrt{2}=12+6\sqrt{2}$
$=6(2+\sqrt{2})$ units.

So, option A is correct.