The perimeter of the triangle with vertices at (1, 0, 0), (0, 1, 0) and (0, 0, 1) is

Question

The perimeter of the triangle with vertices at (1, 0, 0), (0, 1, 0) and (0, 0, 1) is (A) 3 (B) 2 (C) 2√2 (D) 3√2

Tardigrade Admin · Accepted Answer

Let A = (1, 0, 0), B = (0, 1, 0) and C = (0, 0, 1) so, AB=√(0-1)2+(1-0)2+02=√2 BC=√O2+(0-1)2+(1-02)=√2 and CA=√(1-0)2+02+(0-12)=√2 ∴ Perimeter of triangle =AB+BC+CA =√2+√2+√2 =3√2

Q. The perimeter of the triangle with vertices at $(1, 0, 0), (0, 1, 0)$ and $(0, 0, 1)$ is

$3$

$2$

$22$

$32$

Let $A = (1, 0, 0), B = (0, 1, 0)$ and $C = (0, 0, 1)$
so, $A B = (0 - 1)^{2} + (1 - 0)^{2} + 0^{2} = 2$
$BC = O^{2} + (0 - 1)^{2} + (1 - 0^{2}) = 2$
and $C A = (1 - 0)^{2} + 0^{2} + (0 - 1^{2}) = 2$
$∴$ Perimeter of triangle $= A B + BC + C A$
$= 2 + 2 + 2$
$= 32$

Q. The perimeter of the triangle with vertices at (1,0,0),(0,1,0) and (0,0,1) is

3

2

22​

32​

Let A=(1,0,0),B=(0,1,0) and C=(0,0,1) so, AB=(0−1)2+(1−0)2+02​=2​ BC=O2+(0−1)2+(1−02)​=2​ and CA=(1−0)2+02+(0−12)​=2​ ∴ Perimeter of triangle =AB+BC+CA =2​+2​+2​ =32​

Q. The perimeter of the triangle with vertices at $(1, 0, 0), (0, 1, 0)$ and $(0, 0, 1)$ is

$3$

$2$

$22$

$32$

Let $A = (1, 0, 0), B = (0, 1, 0)$ and $C = (0, 0, 1)$
so, $A B = (0 - 1)^{2} + (1 - 0)^{2} + 0^{2} = 2$
$BC = O^{2} + (0 - 1)^{2} + (1 - 0^{2}) = 2$
and $C A = (1 - 0)^{2} + 0^{2} + (0 - 1^{2}) = 2$
$∴$ Perimeter of triangle $= A B + BC + C A$
$= 2 + 2 + 2$
$= 32$